I think that's just a guess/speculation on Danhauser's part. While that door was there in TAS, I don't recall seeing that second exit ever actually being used (or shown to lead to a turbolift) in a TAS episode. (Someone who has watched TAS recently can certainly correct me if I am mistaken.) IIRC, the first time we actually see a second turbolift entrance/exit to the bridge is in TMP.
AFAIK, you are correct.
However, TAS production was error prone, and one of the errors was that door cels were sometimes forgotten. For example, at 14:49 in
Beyond the Farthest Star, they forgot the door for the second exit, so you can see what's behind the door. It looks a lot like a turbolift. So, even if that's all Danhauser is going on, it looks like a really good guess, I think.
Even so, whatever the exit was supposed to be for in TAS, I was wondering whether its addition was in anyway related to the FJ plans, or the source material that FJ used.