I agree the rule should be absolute, but the flip side irony is that the site does not declare some drawn positions a draw, not just "drawish", but DRAWN:
This position is DRAWN, but the site declares who ever ran out of time to have lost. When you no longer have an obligation to make legal moves, the amount of time left is irrelevant as the game is already over.
I have noticed however that the "checkmate being possible in anyway" is not foolproof on this site either:
I got a draw out of something like this playing white when my time ran out (I was actually winning by a couple rooks but just started making random moves to save time, I played slow and screwed up later blundering both rooks, but technically black can mate white, if I move my king to a similar position to the puzzle I posted earlier in this page, trying to defend my pawn. I think the rule the sight implements is that if the side who still has time doesn't have sufficient material if white just had the lone king, it counts as a draw even if white doesn't just have a lone king. But I am not against amending this to allowing a virtual arbiter every 25 or 50 games where you can appeal your time loss.