That's wrong though, the employer is responsible, unless it's the pilots aircraft. Pilots are only responsible for the safety of passengers, they are not legally liable for anything that happens to them. That falls on the airline.
However, as the airlines say they are ready to fly, then the airlines own insurers would have OK'd the flights as safe, they certainly aren't going going to risk even a small % chance of having to pay out £100's Millions
3 Major volcanic incidents in 30 years says it all really, and they flew through the main cloud, not over a 1000 miles away.