"Охотно верю" значит, что он верит?
Kind of.
If somebody says "охотно верю" -- more often than not some "but" follows. In your case, he says that he believes her, but it (that he believes her) doesn't matter much, because what happened, or rather not happened, was a fluke ("Но ведь могло же быть?" -- refers to past) and even if it didn't happen in the past it may well happen in the future and this is what matters.