Whenever you run out of time, you lose, no matter the position
In a recent game, I ran out of time

His opponent only had a king, but he didn't mention his own pieces. Ff he had enough pieces to checkmate, then if his time runs out, he loses. So no, I'm not wrong.
When it's insufficient material, the game ends automatically, you don't even run out of time.
In a recent game, I ran out of time, but my opponent only had a king left. Should this have been a draw?