Earlier quoted context omitted.
I can't find any trace of such a thing, do you have links? What would it even mean to "log in" if they reject my authenticator ? Logging in is what it's for.
You have to log in with your password, of course. And then re-enroll your authenticator.
But also you presented no evidence they can somehow detect their problem and try to ask for the password even if it would help them.