I spent five hours on the phone today with an Apple senior associate and an Apple engineer in the media services department. They were explicit that the fraud prevention department had placed notes on my account with instructions that it should not be reactivated due to violations in the T&C, and that the violations were related to the use of Apple gift cards. So, yes, we're pretty sure it was the gift cards, although it's likely there are some details that I'm not aware of.
They probably have algos that surface fraud-like behavior which is then reviewed by a fraud specialist. I'm sure Apple has to battle massive amounts of fraud. It's a hard job, and it's understandable that in some cases there would be an immediate and irrevocable ban. I'm just astonished that it happened to me.