I guess high school teachers can get away with mentioning the A as a global rule simply because high school music rarely has a key with sharps. You're usually playing in a key that uses A-flat instead of A, or it's the third on an F or the sixth on a C or a seventh on a B-flat. Playing that sixth a little sharp might or might not be wrong, but it's unlikely to be a held note of a chord in high school repertoire. The seventh might be part of a chord, but that's going to be pretty crunchy for high school curricula.