You're absolutely right.

The reason I don't find his claim about not being billed unbelievable is that the IRS got their court win, which is probably what they really wanted.

Billing him would open up an opportunity for him to relitigate the issue by not paying that bill. If his argument has held up in court multiple times, then it's probably not worth risking that you might lose the precedent that was just won, if you're the IRS.