It is true that DoJ's antitrust laws are more long standing and therefore their authority, scope and power is clearer and has been tested over 100 years by courts.
However, it is not specific to the airline industry.
I think that the very reason that Congress gave the DoT the power that it has to review code-shares (untested and vague as it may be) is precisely because the DoJ's antitrust analysis tools were inadequate to address the airline industry. (I'd agree with that)
So, DoT definitely has authority.... how they can enforce it, what are its limits I do not know.... even more important, I don't know how much this stuff has already been determined.
I'll do some more research.... slowly.
The fact that they are going before an administrative law judge is interesting. It would appear to me that there is an administrative procedure for the agency to make a determination... so there must be something of administrative action to 'determine' Why go to an adminstrative law judge to determine a meaningless point? THAT'S WHAT COURTS ARE FOR! : )
But stranger things have happened.