I had a similar situation during the volcano debacle of 2010. Air France refused to issue me a proof of no-show for the second flight (which was cancelled anyway; they all were), but luckily, the proof of cancellation of my first flight on another airline, as well as the receipt from my rebooked itinerary via a different route, were enough to satisfy my insurance company.

I think that the confusion stems from the fact that some airlines do, indeed, issue a "proof of no-show" letter on request. (e.g. Ryanair) so the insurance companies assume that all airlines will issue one, and thus require it. Try asking your insurance company if alternate documents will serve as proof, e.g. the rebooked flight that you were in fact on, or evidence of the delay of your first flight, which would show that you couldn't possibly have been in two places at once.