This is what I had thought might be the problem. That he was offended by your not believing him. I had problems accepting the quick judgment that some others made that his anger was proof that he was acting inappropriately knowing full well there could have been other reasons for this.

I'm glad he expressed his reasons honesetly with you.

AT this point your worries should be a bit less about how to apologize because he obviously didn't tell you he was hurt just so he could write off the friendship but hopes that you'll understand. Meaning: he will be open to apologies, if you feel you need to.

I cannot say how you acted was offensive or wrong. But if you feel the brunt of the responsibility for it, then I only think that if anything, perhaps you handled it wrong is all. With that I would approach it without apologizing for misunderstanding, that does happen but in how you brought it up to him. try to come to an understanding that if you feel he has made a mistake you will approach it more sensitively assuming not that he is already guilty but giving him a chance to explain and to trust his answer.

This misunderstanding really was all about communication. Your mistake was not taking him at his word, his mistake was not voicing his being hurt without anger and overreacting. Keep in mind you are both responsible for your parts in the dispute. I think you both need apologies.