I looked in the USCF rulebook, and I think the wording there is questionable, especially rule 14D4. However, the intent seems clear enough. I’m not sure it’s so clear that it ought to be called “common sense”, though. I don’t think it’s extremely obvious what to do.
Thinking about 14D-14D3, I think the intent of the rulebook is to state that if those conditions exist, the game is an automatic draw. So, for example, if the board has King v. King, it’s a draw, period. It doesn’t matter if anyone resigns. It’s a draw.
Where it gets confusing is that the TD tip under 14D refers to a claim.
It seems to me that no claim is necessary. If it’s K v K, it’s a draw, claim or no claim. It seems to me that the TD can step in and call it a draw, without waiting for a player to claim it.
Of course, unless a TD is standing there watching, someone who wants to invoke the rule would have to call one, which I suppose is making a claim.
Then you get to 14D4: “There are no legal moves that could lead to the player being checkmated by the opponent.”
The problem is that it refers to “the player”, which leaves some doubt as to whether this is supposed to apply to one player, or both. So if white has K+R, and black has K, there are no moves black can make that would lead to white’s checkmate, but there are moves white could make that would lead to black’s checkmate. “Common sense” would say that in this case there is no automatic draw that the TD could jump in with. On the other hand, it sounds like it is saying in this case that white could claim a draw. 14E makes it explicit that if white’s flag falls, it’s a draw.
But what if white resigns in that case?
It seems to me that the player has some agency in this case. He resigned. It should count. I don’t see any rule to contradict it. The game was going on. There was no automatic reason to stop the game. One player resigned. I think that rule 13 carries the primary weight. If the game is going on, and one player resigns, that player loses. If, on the other hand, the game is already over (for example, due to rule 14) the player can’t resign.
As a TD, I think I prefer that way, too. I don’t have the awkward situation of telling the person whose opponent resigned that I am overriding the resignation because of the board situation. Perhaps, as in the anecdote described in the first reply, the player was just throwing a tantrum and walked away. In that case, I don’t have any objection to accepting his resignation.
The FIDE rule overrides that agency, though. Therefore, “common sense” or not, there’s a rule, and the rule overrides whatever you think common sense ought to be. In the FIDE case, if you resign in a position where your opponent can’t win on the board, it’s a draw.
ETA: And…if both players were young children, I would handle it like Jeff did. In a non-USCF tournament for our school chess club, when I was directing that’s what I did. Some of the other adults present wanted to jump in and help teach the player with K+Q how to achieve mate, but I insisted that this was a tournament, and if the kid didn’t know how to win the game, it was a draw.