(This is a serious question - I imagine there are real reasons why not, I just can't think of any myself apart from inconvenience/general principle).
You'd probably have an inkling that their authentication is based on Facebook, so the photo ID thing is highly unlikely to work. (It seemed to be said more to counter the clerk's statement of not being able to validate users than a proposal of a real solution).
The clerk actually provided a real, practical solution (fake account) that the author does not seem to think very highly of.
You could buy a throw away cell phone for verification, which is what some people do after I did a little research, but it's more effort than I'm willing to spend.
These were not obvious fake accounts, I create a realistic fake name, location, and a couple of interests. At the time, it seemed all new accounts would require a phone number shortly after registration. I imagine it's still the same.
In conclusion, I just don't use Facebook. If I'm not willing to bend over and give up my privacy, they don't want my business. So, I don't use them, and don't implement anything Facebook related across my sites.