"There are NOT any bullets on the screen" should return true.
See it's not really "There are NOT any bullets on the screen", it's more like "There are (one or more) bullets that are not on the screen".
You're not asking "are there no bullets on the screen?", you're asking "are there any bullets not on the screen?".
It's like the condition "Player: NOT Platform is moving" will be false if there is no player object. It's not "are there no players moving?", it's "is any player object not moving?".