The swim cap is literally, a mini wetsuit for your head. It is basically rubber and it floats. If you don't believe me, take it off and throw it in the water. That is added buoyancy for your head which makes your head float easier.
Swimming requires a great deal of sensitivity and your body receives a great deal of feedback. That extra 1-2mm on your head is a huge change!
I just had one of my triathletes who is new to swimming return from Costa Rica from vacation. He swam every day for 10 days down there. When he returned and jump back in the pool, for the entire session he was completely out of whack, off balance and uncomfortable. He emailed me very concerned that he "forgot" how to swim. I told him not to sweat it and that he just became very use to the buoyancy of the salt water. It took him two pool sessions just to become familiar again with pool water.
Thinking you are cheating by wearing a swim cap is like saying it is cheating wearing a swim suit and a pair of goggles ;-p