From my observation, that’s correct.
The flying AI aircrafts uses a completely separate aircraft models, and not using the same aircraft models as the one in parking.
the only way to get the flying aircrafts use the livery is to have a separate livery that applies to those models. I think this is very rare as livery modders only create liveries for the flyable aircrafts and not the flying AI traffic.
I found this that adds traffic liveries. but since they’re separate, they keep track of its own livery library than sharing it with the ones you already have installed. Live Traffic with working Liveries!