After all, Kirk didn't wear the yellow uniform until the end of the movie, he was mainly wearing the black shirt, so uniform variation is possible.
He was wearing a black shirt because he was unauthorized cadet on board a ship. He had no ranking, no position, and no division.
AFAIK, the black shirt is part of all TOS uniforms (at least in the Abramsverse). They all have the black shirt underneath an outer one in the appropriate branch color. So Kirk was, technically, wearing 1/2 of a uniform.
And he did have a rank (Lieutenant), according to the transporter readout screen when Chekov is trying to beam up Kirk and Sulu.
With the black shirts - yes, i know.
All graduating cadets were Lieutenants Junior Grade -- but they were still cadets (Uhura was not referred to as Lieutenant but as Cadet). Fact still remains that he was unauthorized thus, on the Enterprise, he had no rank (ie command) so he only wore the black shirt for the reasons listed above. If he was authorized, he would have been running around in the command gold with the rank insignia of Lieutenant and his little command pin.