BASSA did indeed refuse the requests from BA. To quote at least two cases I have knowledge of, an HKG and a BGI where an empty aircraft was sent to rescue stranded passengers, the aircraft was only available for a fixed number of hours before slotting back into the normal revenue operation, between 24 and 36.
BASSA refused the company's request to have a crew position out on empty aircraft, then take minimum legal rest and operate home with stranded passengers. Their rationale: if you are the only crew on an empty aircraft, you have duties to perform, therefore you cannot be considered to be positioning, but operating, Therefore no alleviation.
Any BASSA-sanctioned crew would have required 24 hours off after positioning out on an empty aircraft. This would not have worked. Hence the solution the company arrived at, that allowed the aircraft to operate. Minimum legal rest was taken, and the flights operated, and the passengers returned home.
Another triumph for BASSA, a "modern and progressive union" to quote from their webpage.