I asked a lawyer this very question and this is my best recollection:

It's all about intent.

If you have an accident flying for a company, you are an agent for that company and are covered under the company's liability umbrella. So long as there was not a gross deviation from the FAR's, company FOM or pilot handbook that was intentional, you are covered.

So, unless you intentionaly try to take off w/out flaps where flaps are required, or intentionaly land in the middle of a thunderstorm when the airport was closed and you were warned not to, you are covered.

Also, if you intentionaly do something gross and have an accident, your personal liability policies may refuse to pay as well. A personal liability policy would cover you if you crashed a private plane on a personal flight, but again so long as you met the requirements above.