Sierra, according to the original post, this family is now using the receptacle in the light fixture, so the loads must not be a problem. With this in mind, let's imagine they will have children in this bathroom and they can't or won't spend the money on a new circuit.

Now, at some point you could have installed a not so code proper GFCI receptacle to take the place of this cheap non compliant receptacle but refused and a child was electrocuted, how would you feel?

I know that was not a fair question, but if you were in Cvelectrics position, some soul searching might be necessary.

Another FWIW, when I said I would do it, I surely wouldn't expect all others to jump on my wagon for obvious reasons.

Roger