They take offense to someone telling them that they could do better and get better.

A lockbox in one neighborhood can go untouched for months while in another neighborhood criminals are brazen enough to do their work in plain view at the front door

Even if your town is heavily leaning towards criminals, there are prison guards, school teachers, attorneys, small business owners, city employees, and other professionals that need quality housing. 

Results are nearly instantaneous (although, if something comes up on their background/criminal reports, the details can take another 15-30 minutes to arrive).  

The whole income source as protected class is the only thing offensive to me.

A few weeks later there is a "guest" staying there, who just happens to be the tenant's boyfriend, who just happens to have a criminal record and would not pass the screening...Now, I'm NOT at all saying or implying that this has any similarity to your situation.

I use rentmonitor.com it can be used to collect app fees, provide credit and criminal background check, automatic late fee collection etc.

Risks add up.Perhaps there's a 1% risk for each visit, a one in a hundred chance that some local person will idly tell their criminal buddy about the nice lady who comes each month and walks away with cash, and their criminal buddy will decide to mug your mother-in-law.

What criminal and civil background check issues are not OK?

Forgive my offense.