I don't see anything in the story that mentions doctors' tax IDs being stolen. Most doctors are incorporated or part of an orgainzation that is, so the tax ID is not a personal defining number.
Many businesses print their tax ID numbers on their bills, requests for proposals, and other documents. My cellular bill shows the tax ID number for AT&T Mobility, so it's not usually a big secret.
I just looked at the doccument my doctor gave me for my last visit where he checks off the services he performed and which is also the form for the Medicare billing and it has the name of his LLC shown prominently and just under their name is printed their tax ID number.
Wes Leatherock firstname.lastname@example.org email@example.com