DUH!!!
Thank you for the reply, Michael. (And also Artichoke, in passing.) I appreciate the perspective.
I can see where there may indeed be times where positional understanding could be helpful in guiding a TD in investigation of a claim being made. As you say, pointing one in the direction of where to ask focused questions, etc.
I think my point, though, is that the TD does not have to look for any further evidence…
In the case at hand both sides readily acknowledge four plies have been made since an illegal move, however you want to slice it.* (Unless one concludes that the TD Tip to rule 11A on Illegal Move with Check might by extension imply that every move after a null move is also an illegal move. That, to me, is a stretch.) At any rate, no positional understanding is required to apply rule 11D1a here.
The only other question to me might be, “Did White cheat by pressing the clock twice?” For which there is no direct evidence or witness evidence. Even if one concludes that White did double-press the clock, there is a big stretch to reach across before ruling that White has cheated: intent.
I could see if you were also suggesting that positional knowledge might supply the TD with a clue that there is motive, means, and opportunity for White to have done it. But that establishes a circumstantial case. The TD might want to keep an eye on that player for the rest of the tournament as time allows / spread word to keep an eye on that player if multiple TDs. But does a TD allow circumstantial evidence to rule a forfeit win to Black? Would that be upheld on appeal? Or must a TD possess direct evidence of cheating - which to my mind might require the burden of intent as well?
And, even then, the four plies played would convince me via 11D1a that both sides have accepted the illegal move, intent or no.
But that’s just my long-winded opinion.
[size=90]*And a P.S. to my long-winded opinion. If one understands the “null move” by White was an illegal move, Black has played g3 and g2+ - two moves by the opponent of the illegal move. If one understands Black’s g3 as the illegal double-move, White has played Kh1 and Kg1 - again two moves by the opponent of the illegal move. And 11D1a is pretty clear that if two moves have been made by opponent in sudden death time pressure, the illegal move stands and no clock adjustment is made.[/size]
On third thought, this also provides a teaching moment to Black. Even in time pressure, and even with a calculated win on the board, one does not move by autopilot and bang out the moves. Or if one does so, one does so at one’s own risk.
That is really just my very most humble opinion.
Calling the knight a “horsie” is like running fingernails across a chalk board… 
Being the good little TD, I ignored the position and just followed the rules discussion. But finally I got curious about the position itself…why does Black believe he has calculated a win? Perfect play by White holds the draw, does it not? Plus, if Black is paying attention, and not just imagining his glorious victory in his head, Black should have played Kg3 if White didn’t move. NOW he has the opposition, and now Black can win! Or am I missing something?
Ding! Ding! Ding! We have a winner!
I think you may have missed something.
Initial position as described, Black to move:
Analysis:
[Event “K-12”]
[Site “USCF Postgame Analysis”]
[Date “2009.12.16”]
[Round “?”]
[White “NN,White”]
[Black “NN,Black”]
[Result “*”]
[SetUp “1”]
[FEN “8/8/8/8/6p1/6k1/8/6K1 b - - 0 1”]
[PlyCount “6”]
1… Kf3 2. – {?? As played, null move.} (2. Kf1 g3 3. Kg1 g2 4. Kh2 Kf2 5.
Kh3 g1=Q {± 1-0}) (2. Kh1 g3 3. Kg1 g2 4. Kh2 Kf2 {± 1-0}) 2… g3 (2…
Kg3 {Still wins - just the same as before.} 3. Kf1 Kh2 4. Kf2 g3+ 5. Kf1 g2+)
3. Kh1 g2+ 4. Kg1 Kg3 {stalemate} *
For the non-computer…
1… Kf3
- – {?? As played, null move.}
(2. Kf1 g3 3. Kg1 g2 4. Kh2 Kf2 5.Kh3 g1=Q {± 1-0})
(2. Kh1 g3 3. Kg1 g2 4. Kh2 Kf2 {± 1-0})
2… g3
(2…Kg3 {Still wins - just the same as before.} 3. Kf1 Kh2 4. Kf2 g3+ 5. Kf1 g2+)
- Kh1 g2+ 4. Kg1 Kg3 {stalemate} *
(in the 2. Kf1/Kh1 lines, 3. Kh1 is met with 3. …Kf2 4. Kh2 g3+ and Black still promotes…)
- … Kf3 is a mistake, but Black still wins since he can repeat the position and make the right move. 1. … Kf3 2. Kh2! Kf2 3. Kh1 Kg3 (not 3. … g3? stalemate) 4. Kg1 and now the correct 4. … Kh3! 5. Kh1 g3 6. Kg1 g2+ wins. This is essentially #28 in Averbakh’s “King and Pawn Endings.”
You see, this is why I shoot my mouth off. So I can learn when I think someone else missed something, but in fact I missed something. 
And, parenthetically, an object lesson in TDs considering things on the basis of the rules and not the positions.
See how dangerous it is for TD’s to count on their chess skill when making rulings?
Yup, but that is exactly what the young player claimed - well after I edited the post that is! 
Extending that logic, it is equally dangerous for skilled chess players to trust TD’s to make correct rulings in their games. Now do you know why I always insist on using time delay?
Michael Aigner
No, I don’t.
14H claims, I assume. And I would agree with that.
I have been consistent by saying that circumstantial evidence gives the TD a reason to ask pointed questions in an effort to find out more. I admit it is conceivable that white might have cheated and yet could talk his way out of it. Personally, I find this unlikely, especially with younger kids. It is very easy for a player to stumble in his explanations, allowing the TD to determine who was speaking the truth. I’ve even seen this in adult tournaments.
Given the possibility of deliberate cheating based on the specific nature of the position on the board, the TD must complete his due diligence before he rules “the parties can’t agree on what happened, therefore the game must continue as is.” (In this case, the game ended in stalemate.)
I completely agree. Black could have and should have made a claim immediately after white pressed the clock without moving (assuming that’s what happened). By the way, we don’t know exactly how much time is left, other than that both players were under 5 minutes.
However, I am equally concerned that one of these two kids may end up learning the benefits of being dishonest. There simply are too many warning signs for the TD to ignore. I am convinced that the truth was merely one or two questions away. Did black press the clock incorrectly, or did white take advantage of black looking around the room?
Michael Aigner
I’m having trouble with your reasoning. Neither player made a valid complaint. The TD is expressly forbidden to intervene is such a situation (see 11D1). In my opinion, for the TD to press the issue would have been a violation of 21K2 (Beware abuse of power). Perhaps you think the rules should be different, or different for kiddie tournaments. I’m dubious, but it’s a valid point for discussion. Given the rules as they are, however, I don’t see any way to reach your desired result.
Does this qualify as a valid claim or not? For the moment, ignore relevant issues such as the stalemate, two moves having been played, and the timing of the claim. Is “my opponent pressed the clock without moving” a valid claim?
Now that we’ve answered that, we can get back to addressing the multiple interesting issues. I am ready to hear what the staff in Dallas concluded.
Michael Aigner
No, because it was not made before the end of the game. Stalemate ends the game. With a few limited exceptions, none of which apply here, a claim made after the end of the game is not valid. I don’t see how I can state it more clearly. Now, if your question is whether it would have been a valid claim if made before the stalemate occurred on the board, well, that’s fact-based and cannot readily be answered as a hypothetical. I can construct scenarios in which it would get a penalty, and others in which it would be dismissed as frivolous.
Wait. On one hand, you say no claim was made by either player. On the other hand, you seem to rule that the game is over due to stalemate.
At the very least, a stalemate ruling requires you to verify that the last move played was indeed legal. But you wouldn’t even bother doing that, since you say no claim was made. Surely you’re not encouraging the TD to interfere when no claim was made.
I interpret the last sentence of the OP that the assistant floor TD thought this example required TD intervention and a ruling.
Yes, I admit that upholding the result of the game is, in fact, one possible ruling. I disagree, but I am eager to hear what actually happened.
Michael Aigner
No one claimed that the last move was illegal. The only claim made was that, at an earlier point, one player may have made two moves in a row. That claim was made after the game was over, and thus had to be rejected out of hand. That was why I was careful to use the word “invalid.” For that matter, even if the TD had seen an illegal move, he would be forbidden to intervene unless one of the players made a claim either a) before the stalemate appeared on the board, or b) immediately after the stalemate, if and only if the claim is that the last move was illegal. Neither of these was the case, so the game is over and there is no recousres. If the floor TD ruled otherwise, he was mistaken.