Q: Does the Rule Mystery Play require one to play the specific card flipped up from the top of the deck?

My friends think you can add it to you hand, and play some other card from their hand.

A: You are correct, your friends are incorrect. You pull the top card off the deck, and immediately play that card. You do not get to add it to your hand, or play any other card from your hand.

Also see: What are all the different cards in different versions where you get to draw the top card and play it immediately?