Earlier quoted context omitted.
"Apparently after I had left, someone went into a T-Mobile store and somehow convinced the associate that my number was theirs." How that can happen? When I visit my cell provider's store, nobody is going to talk about any account details while you haven't provided a government issued ID to prove that you are an account holder. Sure, it's not 100% bulletproof method, but if somebody went a great lengths to counterfei…
Yes, ID check is easily circumvented. People are the weakest link. The store reps are not government officials or police officers, nor do they scan ids. They may be convinced not to check your if, accept an id that isn't your drivers license, or anything else. The point is that by using an SMS as 2fa, is placing much of your security in underpaid cell phone store workers.
Neither they are here (in EU), but nobody is going to talk to you unless you provide an ID anyway. Asking for ID doesn't seem too hard, even for non-trained personnel. You don't have to be a detective to match name/code on ID with the name/code on account.