I've been ripped off a couple of times and the only time I had to produce receipts or serial numbers was when my entire system was taken (amps, head unit, crossovers, cap, subs, etc...) because we were talking lots of cash there. The got my crossovers and not my components so I ended up getting the shop I purchased them from to make a cost estimate for new crossovers only, at the time you could only get crossovers as a package not individually like you can now. I ended up buying an engagement ring with the money. The other times it was just me telling them I paid X amount for what ever and they took my word.
The last time I was ripped off was in my Jeep Cherokee Classic and they got my head unit. The insurance guy wrote me a check on the spot for (a new window + head unit) - deductible. They broke out the little triangle window in the front which oddly enough is the most expensive. All I did was find one at a junk yard for $20 and pocket the rest.
If the shop installed it then they should have records from the install. I know places say "free install" but I find it hard to believe those guys work for free
If you installed it your self ask the insurance guy (or woman) to come out and look at the whole in your dash. 22yrs as a customer should mean something but sadly doesn't seem to in your case. Raise a little stink about being a long time loyal customer, etc… Ask for them to show you in the policy that you signed where it states that a valid receipt has to be shown to be able to file a claim. Also ask them if you were able to produce a receipt what steps would they take to prove that it was valid? Because with a little bit of time and some Photoshop anyone can produce a receipt that “looks authentic”. Also if it was stolen at your house you can look at claiming it on your home owner’s policy.