xor7ommy,
Your question seems to be about determining the tonality of music. Is it determined by the diatonic chords? Is it determined by the scale/key being used?
I think the thing to consider is this: if the music is truly in a major key - let's assume C major - then the tonic chord C major should have some special importance. Usually that importance is achieved by starting and ending the music with the tonic chord and ending many phrases on the tonic chord.
If the tonic chord was not emphasized in this way, I think you would get the result you suggest. The music would not seem to be in a major key. So again, using the key of C major, if we emphasized the d minor chord in our phrasing, the music could start sounding like it was not actually in C major, but rather in D dorian.
So, I don't think tonality is defined simply by which diatonic chords are being used, but which ones are being emphasized.
A few asides:
Composers like Satie, Debussy, and Ravel played around with the diatonic series emphasizing different sounds, not quite major or minor, but sort of modal.
A related term is "Pandiatonicism."
A fun experiment is to play only major chords over the roots of a major scale. So, in C major you would be playing chords: C major, D major, E major, F major, etc. This will definitely not sound like a major key. This sort of demonstrates that a major key is not comprised of only major chords.
Interesting topic!
Mike