No proof of purchase is required to report a stolen gun. If you have a SN and a description of the gun you will not raise any suspicions. If you report a SN you just make up and when LE enters it and it does not match the description of the gun you reported it will raise red flags.
You could get info from a gunstore, etc, but when those guns are sold there is a paper trail and security cameras in most stores that would make it easier to get caught. It would never work on a new gun. The older the gun, and the more times it has changed hands the harder it is to track and the better candidate for a scam artist to use.
If someone is pretty smart about this the odds of getting caught are slim. Someone could cruise the net looking for someone bragging about a gun they just inherited from grandpa and posting photos. More than likely that gun will never be sold, or ever have the SN ran by LE. At least not in my lifetime. That is the one I'd report stolen as mine.
Or look out for the guy who brags about his newest gunshow find bought in a FTF transaction from a stranger. If I were dishonest I'd immediately call the police and my insurancee company to report that I had just discovered my gun missing from my car. I'd say it was last seen 2 weeks ago, and was taken sometime during the last 2 weeks. Even if the SN gets run the current owner cannot identify who he purchased it from and has no way to prove he did not unknowingly buy a stolen gun.
Remember, they are not trying to accuse you of stealing their gun. They are betting the numbers never get run and no one will ever realize it. They just want the insurance money. If the SN does get run at some time the odds of them getting caught increase. Very, very few guns ever have their SN's run unless they are used in a crime.
I'd bet if every gun in the country were required to be registered you'd be surprised how many have been reported stolen that were actually not.