By that logic, any specific episode might not be in the Prime universe. We might as well say that there is no proof 'Spock's Brain', 'Code of Honor' or 'Threshold' are in the Prime universe due to the poor quality of those episodes.You are assuming Prime, Mirror and Kelvin are the only universes that exist. Within Star Trek we already know that is not true.
Episodes with dialogue errors like "Klingons joined the Federation", Data's "Class of 76" and more could be attributed to parallel universes by that logic. Insurrection wouldn't take place in the Prime Universe due to Troi's "I never kissed you with a beard before" when she kissed Riker tons of times with a beard in the Prime universe.