I would never have thought of it, and like bella the mere idea seems very foreign to me, like hiring a private investigator to check on someone you've just met. It sounds paranoid and weird, and if I heard someone had done a background check on me, I probably wouldn't want a relationship with them.
This being said, I don't think your necessarily were wrong. He had charges and you wanted to know which, I guess that makes some sense. And it seems "background check" doesn't have the same connotations of "I just had to check if you're a serial rapist before shaking your hand" over there than it does for me or bella, so it might be something he should have expected a bit more.
Since, I would definitely be upfront about that and even do the background check together. Since it was compared to a STD test, I wouldn't go check someone's health record, but I would ask for test result and/or take a new test together.
I would provide mine in return though, so I would say, did you offer your own background checks as well? It seems only fair.
In the end, while I can get why he'd be pissed, I think lying about that to begin with really doesn't bode well, and instead of being pissed he should have been explaining why he lied, apologized for lying, and then said he wished you hadn't done a background check behind his back.