Are you sure?
As far as I know - no BA F passenger pays to reserve a seat.
You're absolutely right - I'm confusing it with 1A/K - which in fairness were the seats in question here - which are only bookable to premium card holders. But that doesn't mean I was right in that they need to pay for seat selection in F!
And yes - overbookings to happen in F - but it could also be a matter of seats blocked for crew rest etc. Not sure abt the BA practice here but other airlines do block even F seats for crew rest. Hope it goes well either way!