Completely wrong. Don't listen to whoever told you that! The pvp , and everything (bar the RMAH) is completely free to use and play. Whomever told you this is completely wrong. Maybe they were thinking of some other game... But no don't be worried it wont cost you a penny!
PvP is related to money because diablo 3 is a game of items. Regardless of what your skill level is, your character requires less and less skill to win the better your gear gets. Buying of items (or playing every day of your life until your eyes bleed) means you win, even if you're terrible at the game at often times. I saw a lot of this happen in wow, which had gold farmers selling gold and an auction house system of its own, plus the obvious- items.
i still hope the pvp changes a little bit more. i'm still not too fond of the arena, i miss the... i guess you'd call it open world pvp? just being able to toggle pvp and charge out at them outside of town. but hey, they always pull through somehow.