The question make sense without ever thinking about piano. The question is: how come the notes named only by letters (without any accidentals) form a major scale, and yet the note A is not the first note (or tonic) of that scale.

The answer is probably related to the fact that those notes also form other scales (seven of them - seven diatonic modes, one of which corresponds to major scale), and it's only relatively recently that the major scale took a central role in music theory.