Probably not quite the best title for this, but here's the problem.
The other day I was jamming with friends and the accordion player pulled out sheet music for "Alabama Jubilee" and said "this tune is in A 7th" - I was kind of surprised, but figured since he reads music and I don't he knew what he was talking about.

I started playing along when I realized it's the same old tune I know as being in the key of C. Where the mix-up comes is that the first three notes are individual pick-up notes that run down from a C note to the A7 (the full chord progression of the song is approximately: A7, D7, G, C, A7, Dm, F, C, E7, F, C, D, G, C)

Now, even though I don't read music, I know that the key is usually the last note or chord that the tune ends on - which in this case is obviously C.   What I got to wondering afterwards - AND HERE IS MY QUESTION - I've never heard of tunes being in the key of a seventh, or a 9th or a 13th, or an augmented or diminished - ie, C7, D9, E +, etc., but I have heard of tunes being in the key of A minor, or E minor, etc.   Why do minors get to be a "key" and the other coloration of chords do not ??