You're right that "modes" can throw some people off. But this is far less likely when they hear tunes than when they read music from dots or tablature. Aurally, the true tonics are hard to mistake, whatever the mode--our making sense of music in customary ways depends on it. We even follow modal shifts, tonic shifts and combinations of the two without difficulty. A person may hear a Dorian tune and just assume it's minor (Aeolian)--albeit a little odd; nevertheless, he is unlikely to mistake where the tonic is. But with written music, we're guided by more abstract mental translations: key signature to major or minor (like there are no other choices.) That's where mistaking the actual tonic is more likely.

Note: The Selchie variants I recall fluctuate between Ionian and Mixolydian, and they begin and end on the fifth, relative to the tonal root. Apparently Baez's is rather different. A more standard example might be less confusing.