I'm relatively new to "the hobby," and don't hobby in the USA because it's illegal in 49 states, so I maybe don't have that great an understanding of either how things work in the USA now, or how they used to work, but ....
As I understand it much of the demand for intense client screening among SPs in the US is recent, and it arose from a 2009 wave of attacks on SPs in Massachusetts and Rhode Island that were the work of the so-called "Craigslist killer". One SP was killed and two others were the victims of armed robbery. The man who was arrested and charged in the killing committed suicide before he could be brought to trial. Needless to say SPs in these circumstances cannot go to law enforcement for help. (A very good reason why the whole enterprise should be LEGAL in the USA the way it is in most countries that aren't run by religious fanatics. But I digress.)
As far as the SP who has her clients sign on to a cam site...there are a lot of urban legends about what cops in the US can and cannot do while undercover. One example is the oft-repeated canard that a cop is required to answer in the affirmative when directly asked, "Are you a cop?" Sounds like she's bought into some urban legend someone told her a long time ago.
I'm not sure how comfortable I'd be with screening data getting into the hands of the police, if a provider or an agency got busted. It'd be one thing if they were to get the provider's little black book with a fake name and the number of a prepaid "burner" cell phone you paid cash for, but as I understand it a lot of the agencies ask for things like your real name, your employer, etc., etc. That could be disaster, especially given that a few states (MA and IL, I think, maybe some others) have enacted "End Demand" laws that drastically increase the penalties for solicitation. In MA for instance solicitation now carries a potential 2.5 year jail term! Hardly the "pay the bailiff on your way out" public-order crime it used to be. I don't know if that's going to change enforcement priorities in those states any but I wouldn't want to be the test case.