I am thinking I should pull one of those old outlets without the third wire and see what’s going on back there.
It sounds like you’re referring to having an outlet with only two spade inlets (with no 3rd for ground). Yes, that was typical in older homes; even ones built in the 60’s. One can many times just replace the outlet with a standard (non-isolated ground) outlet (which uses the conduit or metal clad cable ground), and you’ll then have a NEC rated grounded outlet. This is an affordable needed tool when doing that: