Only the seller is liable for remitting the tax, and held accountable as to the goods he sells.
There in lay the disincentive to cheat. The seller takes all the risks of selling at a tax free price to you. He doesn't know when it is worth your effort to turn him in for not remitting sales tax from your purchase of goods from him.
I have no idea if they're remitting although I suspect most are not or are unreporting. But in any case if I tell the VA authorities about my purchases, then I don't doubt the seller will have remitted enough to cover them. For your system to work, everyone would have to report all their purchases.