Amazon.co.uk are now charging US State sales tax

I frequently buy LPs , CDs and box sets from Amazon.co.uk even though I now live in the USA.
One of the reasons was, that because I live outside the EU, the 20% VAT would be deducted from the price.
I just received notification that my order of the Thin Lizzy Legends box set has been shipped - hooray!
Upon examination of the invoice I noticed that there was a charge for tax which corresponds to the tax rate for the state in which I reside.
Knowing Mr Bezos' reputation for tax dodging in the UK, I wonder what the chances are of him passing this on to the appropriate state tax authorities in the USA?