... his bits could've been recorded separately at any time), and then everyone except Uhura appears in "Turnabout Intruder".
Are they allowed to use a contracted actor in an episode but not pay him for it? Even if he didn't actually do anything that week?
Who says Doohan wasn't paid for his work?
It's entirely possible he came in for looping/ADR for the previous episodes and they got his line out of the way for scheduling purposes. He'd still be paid for it though.
More importantly: if Doohan was not considered a member of the regular cast (and in fact a day player) the show would want to get all the ADR done as soon as possible and in one sitting. The more often the "loop group" (as it's called today) gets brought in, the more money they get paid. If Doohan was a member of the regular cast it'd be different - main cast actors are expected to show up to loop group and don't get paid for it (as they are paid already for being members of the main cast.)
At least, that's how it works today. I can't say if it was exactly the same practice in 1969, but it would make sense to me if it were.