Frankly, I suspect that attempting to operate any F-35 variant from anyone's turf would be a messy failure and would
up the turf good and proper.
Historical note: the AH-56 itself survived the Air Force's challenge, emerging unscathed from the 1971 Senate review of different service CAS requirements. I believe it was the Army's decision, in the light of technical problems and combat experience, to replace the AH-56 with the AAH, which became Apache.