It's normal for some mongers, even experienced ones, to feel paranoid. If you search qualifying, references, etc. there is lots of info on this constantly recurring topic. There is no evidence of clients getting burned from this info. There in fact is more known instances where providers get stalked, wind up in hospital, or orgs get outed so they have to move. The org owners (often main PO) don't want to destroy a very profitable business by letting out that info. I believe they destroy the info after 1 or 2 visits, so that info can't get leaked.
I think guys are especially paranoid because they are already doing something illicit, but the big unmentioned risk is getting outed to a wife. There is an illusion of control over the risk no matter how tiny by saying no to the orgs asking for ID info. Anxiety about ID theft is just a rationalization which can easily be solved by putting fraud alerts at all three credit agencies.
The problem like most fears is that guys blank out fear of getting outed without trying to think about how to reduce the odds of getting discovered by doing something stupid. I think it's common that guys will do something stupid that will flag his wife that he's cheating. Once she suspects, it's easy for her to put a GPS tracker on his car, follow to an apt, see him go up near the hour and return an hour later.