I'm afraid that, if I saw your resume after this, I'd reject it on the grounds of the horrible question without even having to consider the felony itself
Well thank goodness you're not my hiring manager. I would guess you're not a hiring manager at all, but - based on YOUR attitude - one of the basement sysadmins who feels like he is God of all technology and better than 99% of the rest of humanity.
The question isn't all that vague, and when reporting on a conviction one of the issues can be that there isn't much room for explanation. It's "[name] was convicted of X". So you may have a guy who's a convicted "sex offender" when all he really did was get drunk and relieve himself in sight of a playground at 1:00am. Unless you have a chance to explain yourself though - which often YOU WON'T, at least on form-based applications - then you probably aren't even getting to the interview.
I haven't any convictions myself, but I've seen some pretty dismally generic applications forms and "vague" pretty much fits them perfectly. Now, from a hiring perspective, yeah I'd feel a little nervous about working next to a convicted sex offender, but not so much the guy who peed on a tree... the problem being that most people aren't going to get past HR screening to the point where the details could even be discussed.