The question was brought up by Khanthal, and a first answer was given by Arcade. The final answer, contradicting Arcade, came from apegamer.

I also have a question regarding the "up a level, down a level" Screw This! card. It says you pick one player who does not get to put a shtick into play. Does this mean the player who plays the card can also put a shtick into play?

There's also another Screw This! card (I think it's "scream like a little girl", or something to that effect), where you can ask any player for assistance. While it would seem illogical to assist yourself, the card text does not seem to prevent this...