I don't believe that Sharp, Lloyd, Lomax, Wells, etc., ever stipulated or required that a true "traditional singer" sing only truly traditional songs.

To call someone a "traditional singer," in practice, means that his or her traditional repertoire is somehow of interest and all else is tangential.

Suppose I find somebody who sings a wonderful version of a Child ballad never before recovered from tradition. He learned it from an aunt up in the hills, who learned it from somebody in 1899. It's a marvel. Sometimes he sings it as she did, but he prefers to accompany himself on a Fender and add wild riffs and a "wiki-wiki-wiki-wiki-wiki-ooo-aaah" refrain. In fact, the only other songs he performs are in the acid rock genre.

Traditional singer? Or tasteless weirdo? Or both?

Both. But absolutely "traditional singer" in regard to his one trad song performed in trad style. Because that's what we're interested in. We may also be interested in what he likes to do to it, but that's a different issue and has nothing to do with the label we apply to him.