I think the better question is ... Why do you care?
Because they could be staff on a forum that has a general audience of 13-17-year-olds, say a gaming forum, and be a(n un)known sex offender (until you look into them).
Do you want somebody on "the list" to moderate your forum, and thereby, be guilty by association, especially if they use the forum as a gateway to commit another offense? Whether or not the intended audience is 13-17?
"What do you or your staff members have to hide?" is the real question now.
I'm not making any accusations here, but you seem laissez-faire when it comes to a serious matter like this. Why wouldn't you want to know who represents your brand, or even worse, your company, that could all be taken away in a matter of seconds, all because you let someone in that you shouldn't have?
Heck, it could even be a car repair forum and you have a convicted felon of grand theft, who served their time, but end up using their prominence as a staff member to target their next victim.
If you don't find any of those to be serious (I could give more examples, but I hope you get the point), well, that's your choice. This is Another Admin Forum, and as Another admin, I want to know who represents my company and my values.
Edit: I used to be salaried on a big (big) board and had to submit a W-9 for tax purposes. While they didn't have my consent to run a background check, nothing could've stopped them and firing me for a different reason if something happened to pop up (they would have asked for consent because they run as a very strict corporate entity, but I have nothing to hide either way).