Of course they should be moved to a more appropriate forum. Stuff gets moved from the General Forum to the Soapbox or whatever all the time. The OP should probably be consulted before moving one from a carrier-specific forum, tho, to find out for sure whether they do, indeed not want responses from those outside their carrier.
I still maintain that if you can read there, you should be able to post there. Carrier specific forums are great for collecting topics regarding carriers, but if the masses can read them, but not post to them, it's exclusionary and stifles discussion. If someone outside of a particular carrier posts a message that proves they don't know what they're talking about, so what? The response is likely to clear up questions that many readers may have about the same thing. The more we know about other carriers, good and bad, the better decisions we can make about those carriers. Besides, a question borne of ignorance may very well spark ideas and discussion never considered.
I would suggest that the carrier specific forums not be available to the masses, same as the Truck Wash, and for the same reasons, but there are many who may be interested in reading what others at their carrier have to say about an issue, but will not post to a carrier specific forum because they don't want the masses to know who they drive for. Nothing wrong with that, either.
So all forums except moderator forums should be open to all, reading and posting, or at the very least posts that aren't strictly carrier specific should be moved to where they are open to all.