I agree with
golfmad . I don't see why BA would refund the cost of the call.
On a separate note I still don't understand the reference to passport details as they aren't required for an LAX - SAT flight (SAT being San Antonio for those who may not know).
As for the lack of a global 800 number and 24-hour call centre availability, I have to agree on this. It is frustrating. You shouldn't have to dial out of region and struggle to find out which office is open at any given time.