Once you have had genital warts, especially a man, he can be a carrier. A recurrence can occur 10 years later without being unfaithful. I got it from my recent partner who said he had it years ago from his ex girlfriend. He doesn't have any symptoms but have given it to several partners now which is how he knew he is a carrier. If a man has the actual warts on his penis, he has to have them burned off with liquid nitrogen, and it hurts like hell. I was told by the doctor there are 80 to 100 types of genital warts. Once you contract this STD, it can recur during your lifetime without infidelity. A woman has to have pap tests regularly once she has had sexual contact with a man with this history to check for cervical cancer or dysplasia on the cervix. I ended up with high grade abnormal cells and recently had to undergo surgery to remove the top part of my cervix due to the infection. So that being said, there is a strong possibility he is telling the truth, but you will now have to be tested every 6 months for the rest of your life to check for the abnormal cells. Even if you presented with abnormal cells, it may not be serious and can go away without treatment. See a well known specialist to be monitored. If you love this man...you can work this out, it *****, but I would be more worried about HIV. Good luck.
Genital warts can reoccur even with treatment. You can believe him.