if customer A has had twenty of the things in the past year from completely different people ...
That's the trouble with the internet, its easy to get 20 different identities.
I certainly wouldn't want my insurance premiums going up on the say so of strangers with no supporting evidence. And this is where the OP falls down too. There is no evidence for the police to work on.
A few weeks ago someone reversed into our car while we we sitting in it. He now says we hit him. Its annoying as hell trying to prove something you know to be true. Sympathies for the OP, but little the police can do. A better interaction may have softened the blow though.