My partner and I have been in a similar situation with someone she was dating. We met him first as a friend and he was honest about going to jail. When things changed, (We never did a background check) but of course we asked him what he went to jail for.
He didn't lie, and that honestly made all the difference to us, and he didnt go to jail for something small. We kept him in our lives because he was young at the time he went to jail, and because he really was a changed person.
However in the future I really see no problem with doing a background check on someone. I would maybe tell them that I plan to do one, but you did ask so you gave this guy the oppertunity to tell the truth. He has no right to be anrgy with you or your wife that he got caught in a lie.