This is what Timatic lays down as the requirements (my bolding):
Originally Posted by Timatic
Passengers must have:
- a negative COVID-19 NAAT or antigen test taken at most 48 hours before arrival. The test result must be in English, French, German, Spanish or accompanied by a certified Spanish translation; or
- a COVID-19 vaccination certificate showing that they were fully vaccinated with AstraZeneca (Vaxzevria), Janssen, Moderna or Pfizer-BioNTech, Serum Institute of India, Sinopharm or Sinovac at least 14 days before arrival; or
- a COVID-19 recovery certificate issued at least 11 days after the positive COVID-19 NAAT test result. The sample for the certificate must have been taken at most 180 days before arrival.
There's absolutely no mention in there of what constitutes a valid certificate, so I can perfectly well understand the BA check-in agent denying you boarding until the necessary assurances had been received from the Spanish immigration authorities.
Airlines rely pretty much exclusively on Timatic as their bible and defence against denied boarding claims. I'm not going to categorically say that you don't have a valid claim against BA, but it does seem that the actions they took were wholly proportionate to what's written in Timatic, and that it was reasonable for them to take further advice before allowing you to board. It is your responsibility to check that what Timatic says you need, you unequivocally have - particularly at times like this. The airline will not start looking at every website or piece of guidance that's out there, and what you quoted is the US Embassy's interpretation, not even from an official Spanish government source. That is not going to help your case, I'm afraid.
That they cleared you to fly in a couple of hours or so is actually pretty impressive, and if brought before a court under EC261 I would think the airline has quite a solid defence. My opinion is that this is one to chalk up to to experience and the vagaries of travel at the moment - I'm afraid lots of things are being pulled around and it's necessary to accept that if you want to travel you may have to put up with stuff just not running as it normally might.
I don't think I've had a single itinerary over the past 18 months that hasn't changed in some way, many of them by considerably more than the delay you experienced at LHR. It just is what it is.