Well, it depends what you mean by "believe in".
"Friends with benefits" relationships can work out very well for some people, but they often don't work out at all for others.
First of all, people often forget that the phrase does include the word "friends" (it's not "casual acquaintances with benefits").
Genuine friends don't hurt each other, lie or mess each other around. If you can't trust someone and don't feel comfortable or safe with them, that person is not a friend.
In this case, if this guy was having a monogamous relationship with his girlfriend, then he's been lying to her - not to mention lying to you if he didn't tell you at the time that he had a girlfriend. That sets some major warning bells ringing in my mind.
I still really like him
Secondly, it's a really bad idea to agree to a casual, no-strings "friends with benefits" sexual relationship when it's not actually what you want.
I've seen a bunch of people on the boards who agree to a "friends with benefits" relationship while secretly hoping it'll turn into a big romance, then get terribly disappointed when it doesn't.
Often, it seems to boil down to one person not feeling confident enough to say that they want a girlfriend-boyfriend relationship, but instead agreeing to someone else's requests and providing no-strings sex while not really feeling happy about the situation. That doesn't make for a happy or healthy relationship.