If fan film makers want to use it, they should perhaps show the occasional red or blue wraparound on other crewmembers as well, if for no other reason than to reinforce the internal logic of the thing.
I always thought that variant was reserved for captains and above. It does help set the captain off visually from other crew-members, both because of the style difference and the more "true-green" hue vs. the "stealth" green of the gold tunic.
I don't remember ever seeing Kirk wear it when he beamed down, however. Garrovick does on Exeter, though.
Kirk wore the green wraparound off-ship in:
"Court Martial," "The Trouble With Tribbles," "Mirror, Mirror," "The Apple," "Wolf In The Fold" and "I, Mudd."