If the Ionian G major would have been writen =G-A-B-C-D-E-F
w-w-h-w-w-h-w
Then I belive that would show the Ionian G major diatonic scale to be writen with an accidental, or mutated into the Mixolydian.
What I am really saying is dont belive that the diatonic scale in any form has an accidental unless a composer writes it with a note outside the set diatonic pattern regardless of sharps, flats, or naturals.
If I am wrong I am looking forward to examples to prove otherwise.