I think there was a thread recently talking about how dumb this was without discussing with your AME first... there are things that the screenings could find that could toast your medical. If your Doc wanted the tests, they'd order them.
Recently here locally, at least one of these "screening" outfits was charged with various crimes for not even having a Physician on-staff while performing radiological screenings on people, and many people who were "addicted" to such screenings had come back (hint: more money for them) multiple times, and had far higher than the recommended levels of annual radiation -- a Doc would have put a stop to it, thus... the company had the simple solution figured out... no Doc. Just "technicians". Patients saw the "medical looking" facilities and just assumed a Doc was around somewhere... and that someone was looking after their health, not possibly ruining it.
Company is claiming the folks signed their usual waiver, knew there was no Doc present, and they had a contract to provide the service if they showed up and paid.
Generally, after seeing that news report, I think I'll stick to the real Docs and their prescribed tests or ask for a referral to have a test done the Doc hasn't prescribed, before ever dealing with one of these fly-by-nights who has enough money to lease radiological equipment and pay Marketers.
The story and case broke when a tech massively over-radiated a "patient", and the State started investigating the rest of the company's behavior.
Here's the other rub: AOPA isn't making the offer out of concern for your heath; they're getting cold hard cash on the barrel head for referrals, I'm sure. Motivation is all wrong.
What better group to offer screenings to, than a bunch of people scared to death of the FAA Aeromedical system, as they age?
Whichever Marketer for one of these screening companies who thought about approaching AOPA before the others did, and got AOPA to do all the work for them, was brilliant. A firehose of money.