Two observations.
- There is no way that BA, on its own volition, would provide bottled water to the crew based on its concern that the tank water might be bad. In the event that a PAX gets sick and sues BA, imagine the liability (not to say the PR disaster) that would attach to this likely discovered BA concern.
- The crew contracts that I have seen for several U.S. airlines require that the airline provide the crew with bottled water as a contractual condition, not due to any concern on the part of the airline as to crew health. As a result, there is no admission by the airline that the tank water represents any health concern.
Therefore, while possibly disgusting, the tank water is likely quite safe.