Ironically the 'private operations' does seem to circumvent some of the rules which are in place to avoid such accidents.
I wonder how many pilots read the insurance policy in relation to the aircraft that they are flying. They could be surprised where the boundary is between the insurance company accepting liability to the captain having it.
Aircraft on AOC operations can have a proviso that the aircraft is flown IAW the Operations Manual. Should it be operated outwith that then it is not insured.
Punching vertically up through the fog may be OK but if somethings happens which may be or may not be the crews fault the Insurance Company will be looking very hard at how the aircraft was operated.