John Barleycorn is not in a minor key, but rather in the Dorian mode, ie., a scale from D to D with no sharps or flats. Since an F chord can be derived from that mode, it can be used sparingly. And while an Am can be drawn out of the mode, it's too jarring. When tempted to throw in one of these, substitute the C.

If I have a chance later, I'll try to put in a verse with the chords I use. Although I've been singing JB for over forty years, I've been doing it unaccompanied or with concertina for the last fifteen or so and I'll need to bring the guitar in here to get it right. Besides, I've only had one cup of coffee so far -- Tom