"We log the BFR as PIC and either get a signoff or don't."

However, the BFR is normally done under visual conditions, while under a hood. The instructor counts as a safety pilot, and you don't need to be instrument current (or even rated) to log PIC under the hood while in VMC with a safety pilot.

In fact, if the right seat is occupied by a CFI, you can even be IMC on a flight plan. I logged many hours of PIC actual time while dual with my instructor working on my instrument rating.

As for the complex thing, I agree with the above, it sounds as if there may be a loophole, but I wouldn't push it. NE_pilot, your interpretation makes the most sense, thanks.