I've been in this situation with my boyfriend, starting when I met him, 2 years ago. He's always claimed to be very monogamous, but he's very flirtatious and affectionate with women in public, and he tends to have a reputation for being a "ladies man". This was a source of some strife between us during the first 6 months that we knew each other; we had a relationship with an expectation of monogamy at that time. I used to suspect him of lying about certain things, and would call him out on it, emphasizing, "I don't care what you do when I'm not around as long as you're safe about it, but please don't lie to me." He would just tremble and say, "No, I'm not like that. And I don't want an open relationship."
Then we switched to just taking things one day at a time and having no rules, no expectations, and no definition for our relationship. Those were good times, probably because living a more poly-ish lifestyle comes more naturally to me. I was completely in love with my guy, but I got to have some friends with benefits and do some work in the adult industry on the side. I was open and honest with him about everything, and he was accepting, and all was well.
We also went through a "normal friends" phase while we weren't living close to one another, and shortly after I returned to where he was living. We got even closer as friends and talked about everything really openly.
It became clear over time that he was right and everyone else was wrong. If he really did sleep around, he probably would have told me, or it would have been obvious. When we got back together this spring, he tearfully admitted that he had had a one-night stand during the time that I was living in another country and in a relationship with another guy there, and he actually apologized for it (I wouldn't have), saying he shouldn't have been with anyone while he loved me. He knew that I had had A LOT more action than that, but he really didn't care and was just disappointed in himself for not being as extremely monogamous as he'd like to be. There were other things, too, that made me believe him.
Now I think that he really is an extremely monogamous guy who is always perceived as a player by other guys because of what they observe in public - he gets along well with women (partly because he's pretty feminine himself) and he's very flirtatious. His female friends know that he's actually very selective, and monogamous. And these days I find it amusing that his male friends have a different impression of him (and are wrong).