They DEFINITELY do more than just "press" on the genetailia - on my first ride ever on Tomb Raider at PKI, the restraint was jolted into my manhood and I literally almost cried. It was the most painful experience I have EVER had on a ride (and that includes when I sliced my hand open on a ride at SFGAd!).
However, since I do like the rides so much, I just cover myself the whole ride and avoid any problems. :)