To restrict "traditional" singers to only songs they learned from their family is far too narrow imo. It completely ignores the social context that "the tradition" was part of, where people sang to their friends and local community, whether in their homes, workplaces, or in the local pub, and learned songs from each other. To distinguish between a song learned from a relative and a neighbour, in this social context, seems to me to be immaterial.

If Fred Jordan (as we keep using him as an example) learned a song from May Bradley, for example, so far as I am concerned that is part of what I think of as "the tradition".

Fred was not a "revivalist" singer because his roots were not in the revival, although he later came to perform in the revival and even learned some songs from it. In the same way, because my own roots are in the revival, I can never be a "traditional" singer, even when singing songs I may have learned from Fred.

I find the most useful label is to think of Fred as a traditional singer, albeit one with a wide repertoire gleaned from many sources. It is helpful to be aware of his wider musical experience outside his own local tradition, but it doesn't alter his main "label". To "relabel" him for every song he sang doesn't seem to me to be a useful exercise. However we are clearly going to have to disagree on this.