As the sign says strictly 'No Breath Holding' beside the pool and if someone drowns in the pool, the pool owners have a legal get out. As someone can only drown in the pool by forgetting to breath either consciously or unconsciously and the sign says strictly 'No breath holding' then I would suspect that legally the owners could not be prosecuted for anyone drowning in that pool.
If the sign said ‘No Conscious Breath Holding’, then the owners could be prosecuted for an unconscious breath holding incident. i.e. an unconscious drowning incident.