Insurance companies say: Pay us premiums.
When the insured makes a claim? That's when insurance companies run a fine-tooth comb through the rules.
The words "privately operated" merely beg the question. An aircraft engaged in "private" operations today isn't necessarily engaged in "private" operations tomorrow. Does the term "private operations" actually appear in the rules these days?
I would have thought this kind of thing is spelled out in your policy if you insured an aircraft and/or pilot.