So as far as G understands F is monogamous and is cheating on her partner (me).
Well, not to be an old fussbudget, but it would seem that G is not playing perfectly straight here either. If he's willing to participate in what he thinks is a backdoor amour, will he hesitate to cheat on that too if the opportunity arises?
So yeah, I agree with the others: be cautious. There has been a bit of dishonest behavior from more than one angle.