It's not 100% clear from the OP if the passenger has tried to be re-routed via the hotline. There's some ambiguous wording in there with regard to re-booking options. I can certainly imagine BA staff playing dumb as it is a much more convenient solution to just let them wait for the plane to be fixed.

It's not like at this point any EU compensation claims wouldn't be maxed out anyway. Re-booking all of them via your own metal and probably also other carriers' metal would likely be more expensive and messy.

But if I were in the pax's shoes I'd definitely have tried to call and get re-booked very early in the game. Even if I had to rent a car and drive out to Bakersfield, Reno, SLC or something.