An OK doesn't exactly contain a plethora of info. It's generic. It's like, 'He paid, and I did not die.'
A reference is usually more detailed - well, some are. Some just say, 'Yeah, he's OK!' But others will say, 'Yes, John! I've seen him several times over the past few months. He's super nice, and always a complete gentleman.' To me, that is infinitely more reassuring than a generic OK.
If I'm not sure about a guy, I'll take the initiative to email a few of his most recent OK's. Sometimes, a provider will say, 'Oh, well I gave him the OK because he was safe. BUT, watch out... ' Other times, it just confirms that he's good to see.
I'll only require info in addition to p411 to screen, if he doesn't have any references, or only has one or two (and especially if the 1 or 2 references don't reply to my inquiry).