I had a similar claim with VHI in August. ( Due to fly out on Thursday, was very sick on Monday, and advised that flying was out) Got doctor to fill out their claim form on second visit ( charged me 20)
I was surprised at how it all went pretty ok with MultiTrip, and got my refund about 6 weeks later.
I was also on separate flights ( Aer Lingus) and a package for our Italy holiday.
VHI will require a confirmation from the Greek co, saying the date you cancelled and that your refund is Zero. (as well as you suppling all the original bookings and invoices)
Also, phone the airline and they will issue you a similar confirmation, and I got refunded the travel tax, but AL charge a 20 each way cancellation fee, which was deducted from Travel tax refund.
So, I got refunded everything by VHI ( except the Travel tax, of course0 BUT they do not refund the AL 20x2 fee.
I had 2 or 3 back and forth emails with the CXlaims handler but if you include that cancellation stuff, it will go fine.
Overall, it went very smoothly ( this was my first ever claim and thought that they would try every trick to wriggle out, but I was wrong!)