Are they serious with this references, screening, verification stuff?

I agree, I don't think it's to screen out LE. I suspect to it's to screen out certain unwanted customers and potential criminals. I was speaking with a provider I've been seening for about a year. I'd only given her my burner phone number. She said my burner number was associated with an old cell phone number I had used several years earlier. She said the AMPs and agencies regularly exchange customer data and that they "rent" a database with over 3 million phone numbers that goes back more than 10 years. I wouldn't have believed it but she had my old cell number and I don't know how else she would have gotten ahold of it.

I think someone is collecting customer info and that there is money to made in selling access to it.
I believe you. But for years I have been hearing about this mysterious database/ provider forum where they have loads of info on us. And no one anywhere seems to have access to it. There are 10s of thousands of hobbyists and not one has a copy? Still, as Slinky noted, it's kinda silly. Cops can lie despite that silly question providers ask. Lol.
We personally see how some of the girls can't switch n turn against you in a second and even threaten you, now do you really want them to have your personal info?? If they want to do a quick video call or something cool but that's about it.
If you want to create a second identity for mongering verification (only) you can get very high quality fake ID's on line, my under 21 yo son has several that he uses to get into bars and they scan at the bars. That being said, I always try to follow the sage advice of the great Genius and only commit one crime at a time. Possessing/using a fake ID can get you in a bunch of trouble.

I'm also a bit put off by the verification, they want my real name, address, etc, but aren't giving me theirs. I understand safety, but that's a 2 way street, mongers can be robbed on site, and blackmailed, particularly if the verification reveals you have a high income job, are a high value person.

I've done verification once or twice, once was for a porn star so I wasn't worried. The other time I sent a photo that was publicly available online so I could claim someone else used it and deny it was me.

There are also a couple pay verification sites out there, I'm a bit leary about using if their records and servers are ever seized
I've had several amps demand image of a DL and work ID. No way in hell. I'll show the license in person, but no way are they getting a copy. Most of them relent. Some will accept UG or one of the other sites as a reference.

One that I've quite wanted to visit (DDY/CCP) wouldn't accept anything except photos of the documents, so, I've had to pass. Too bad, as there have been several providers there I really wanted to try. But no.

I suppose folks get fake IDs, but I wouldn't know where to begin to look for one...