I think this must be some difference between US and UK law, or at least practice. Over here, if one of your employees does something that causes an accident, that's what your insurance and your legal costs cover. Called Employer Liability Insurance. If it impacts members of the public, that's Public Liability Insurance. There are others, like Professional Indemnity or Motor Vehicle Insurance, and anyone doing serious business with you will ask to see all the certificates. To avoid arguments over which of these is responsible, most companies place all these with the same insurer.
Weaseling out by insurers just doesn't significantly happen (I understand it does so more in the USA). If you smash into someone with the company vehicle, you, and thus the insurer, are liable. They can't evade it by saying you have been prosecuted for careless driving and thus outside the terms of the insurance. Most claims beyond being struck by lightning are brought about by doing something against some law somewhere.