Full deflection = missed approach ???

It is common wisdom, and often common sense, that if a full deflection of a
CDI (or GS) is experienced, a missed approach is to be flown. But a lot of
people seem to think that it is REQUIRED. I have had a CFII tell me it is
required. But I can not find anything in FAR or AIM that states such a
requirement.

Again, in a lot of cases I can understand why to do it. But I can also
imagine others where it might make just as much sense to recover the
approach and not go missed.

Can anyone point me at a rule that requires a missed?