@Steve Babiak
This is a known issue with eviction records, criminal records, etc. The states have removed a lot of the identifiers (last 4 of SSN, date of birth) from the records, for privacy reasons. So now you have just name matches and maybe zip/state matches at best. Makes it real easy to get sued and get the wrong data. Ideally you use a screening company that does the post-verification for you, or you're aware of it and do it yourself, like you did.
@Andrey Y.
You're lucky, I guess. As a property owner/manager you want to make sure your tenant can pay the rent and won't cause trouble, among many other concerns that Steve Rosenberg alluded to. You need to be able to verify that in some way. Could it be that either you're a statistical anomaly OR Hawaii is more of a small town type market? (That could be my NY bias creeping in).
In any event @Elizabeth Colegrove hit the nail on the head (although she knows I am not a huge fan of the buildium/mysmartmove process, heh). You need to put them through the "ringer" on the front end, make sure they are who they say they are, have the money, and aren't known to cause problems. Especially in the more tenant friendly states it's a MUST, otherwise you're stuck with them forever. Also the process itself discourages a lot of the people you don't want in the first place.
@John D. - Is it cash like under the table cash, or cash like 1099/not a steady job/biz owner type cash? Are they "unbankable" or just not salaried? I'm just curious because if it's the second type (just no w2), they're are a ton of ways to verify that income/cash, but if it's under the table, how do you know it's going to keep coming in?