Earlier quoted context omitted.
The security hole there is using SMS as an account reset, which makes it a one factor solution (see other discussions of this in the thread). The error was in that implementation, not in SMS 2FA in general.
The point being that had it been 2FA, it would have been the same hole.
* Applications that take a phone number for one reason (2FA or otherwise) and also use it as a single factor for account reset are less secure in the case of number recyling.
* Applications that do 2FA via SMS do not necessarily do account resets via SMS
* 2FA over SMS is more secure than just having a password to secure an account.
I am sorry your girlfriend had this problem. I would have hoped a business like Facebook would better understand phone number usage. Their penchant for taking as much data as they can and using it however they like clearly burned some of their users here. I hope they have tightened up this hole and that this didn't affect too many people.