HUD is right about arrest records — arrest =/= conviction. IMHO, arrest records shouldn’t even be public unless there’s a conviction, since it’s up to the courts to mete out punishment, not the police. (And encouraging discrimination in employment or housing is punishment, like it or not.)
As far as criminal records, it depends. I’d not rent to a violent criminal or to a thief. But if someone was caught smoking pot or got in trouble for being rude to some blowhard of a cop, I wouldn’t care at all. I’d definitely like to know the whole story before judging anyone.