Of course a song can be traditional and of known authorship. Otherwise we have a ludicrous situation where a song which has been traditional for centuries can suddenly be reclassified as untraditional because an assiduous researcher in the Britisah Library finds out who wrote it in 1656. I appreciate other people can use whatever definition they like, but I would say that a definition is useless if you have to switch classifications in the circumstances I have just outlined.
Surely Bob Knight earlier nailed it in one by writing"What if some of the people know who it's by, and some don't". As he points out, if trad=unknown authorship, then the portion of the population who know the author are quite right to say the song is not trad, and the other half are right to say it is. So where does that leave you?