They are definitely priced together. DDD-BBB on its own is much more expensive than DDD-BBB-AAA. It's a (long) stopover allowed by the fare rules. Yes, I meant "monitor" the flight for booking class availability.

Edit: maybe it was just a case of a suboptimal agent. I called again today (suprisingly I ended up in Basel!) and it was no problem to rebook to a day earlier.