I honestly don't remember what the match paperwork asked, or know what it asks now, but if the question is "Have you ever been arrested for a felony?". And you were, but plea bargained to a lesser charge, or went to court and were found innocent, the answer is still yes. You can than explain the answer. Something done as a minor that was sealed may or may not have to be reported. That's where a discussion with an attorney would be useful.
In the case of the person I mentioned, it seems that the PD overreacted, and the match folks didn't buy his explanation of why he answered the way he did. He admitted to not discussing his situation with an experienced attorney.
You can still get a residency outside the match. He'll probably be fine eventually.