Taken directly from the NABSS site:

In order for a school to be a member of NABSS, they must fulfil the criteria of `Britishness´ published on this website and achieve full authorisation, via British inspection, from the appropriate Spanish authorities.

The rigour of the NABSS inspection system, and of the authorisation process itself, provides a yardstick for parents and teachers, who are choosing schools in Spain.

The National Association of British Schools in Spain insists on regular inspection of member schools and provides continuous professional training for Heads and teachers throughout Spain.

Nabss is held in high regard by both the Spanish and British educational authorities and is consulted on new developments. The Association enjoys a very strong relationship with the British Council in Spain, and Council members sit on the Inspection Monitoring Committee.

Please not that this is affiliated with the Spanish education authority. You are just trying to cover yourselves after saying that private schools weren't regulated, when in fact, they are!