What documents do they require, what credit scores do they allow, how do they verify previous rental history, etc.?

Verifying last 2 years of rental history very important!

We work on the principle trust, but verify.

One of the utilities, South West Gas, based in CA, gave me a hard time putting the account into my own name. after several calls, faxing the court-stamped eviction order, verifying my deed through the County, etc,  the operator finally agreed and started to backdate the account change to the beginning of the process!

Verifying last 2 years of rental history very important!

That's when I just decided to bill for biweekly cleaning and install hallway cameras to verify the rooms aren't accessed by anyone unauthorized.

You can still qualify so long as you have verifiable income.

It's important not to place undue trust in their claims without verifying them yourself.

BUT always trust and verify. 

@Kevin Collins I apologize; my response came out a little rough around the edges and I assume that you certainly have done your homework prior too.... but that is a bit of my point... nothing will change when you go and work with a realtor and find investment properties yourself... figuring out what the property is worth IS PART OF THE ANALYSIS (if that's important to you) and because of this it is no different than other than you should now be verifying what the realtor will tell you it's worth as opposed to what the turnkey is telling you.