I paid sales tax at title transfer time.

Title transfer only requires a stated price paid.

If they don't believe what you paid and decide to question it, they can call you out later and this is how they do it (always wondered how that was done).

Got this stupid letter several months later.

Corruption is the norm rather than the exception, pretty much everywhere.

If I could produce a bill of sale right now, it would put a stop to the inquiry, but I don't have one.
It's no secret such things are easily faked but I would never consider doing that.
The door company I bought the vehicle from went out of business, so there is no getting ahold of anyone.