Well, I'd say that the 1, in a song that's in the key of A minor, is A minor; but that in the NN it's WRITTEN as 6m.Not traditionally in Nashville notation.
Am is your 6m and C is your 1.
The key is still the key.
There are plenty of tunes that are genuinely in C major but have an A minor chord; in that case the 1 is C and the 6m is A. There are also plenty of tunes that are genuinely in A minor, in which case harmonically the one is A minor. You can write it however you like. You could declare that you should write it as if it were in G so the A minor that's actually the key of the tune is a 2min.
But, at any rate, in the traditional Nashville style, they'll write "6m" (or, if I understand correctly, just "6" as the m is understood by the notes of the C major scale). I submit that this tells you it's A minor, but it leaves out information about where the harmonies go from there. To ME, at least, saying "6m-2m-V7-I" means something different than "i min-iv min-bVII7-IIImaj".
But they're not asking me, are they?