Not always the case. My current trip is purchased as a Q fare bucket, and is earning 100% AA miles, but would only be earning 50% QFF points if crediting to QFF. To get to 100% QF points earning I would have needed to pay double the fare price.
And as for earning status, this trip will earn me 20,160 EQM, which is 20% of what is required for Exec Platinum status. Crediting the same fare to QFF would earn me 150 SCs, which is 9.3% of what is required to attain QF Platinum status.
So even with the cheap discount fares the earn rate for both miles/points and status is often better using AAdvantage.
All my trips in the last year have been booked in V, O, Q and two sectors in L, each being the cheapest available fare for the trip I was taking. In fact, I have been booking on codeshare flights operated by QF because they are considerably cheaper than the QF fare. So I get a cheaper fare and better earn rate - that is a win for all concerned.