I really don't understand how they could pay TAX for me?
That doesn't sound right at all.
No one can pay tax in your behalf, only thing they must do is provide papers that states how much are the goods in USD, how much is the shipping in USD and state of origin that goods came from.
Otherwise it could happens that you pay TAX on all that together and that would be very bad.
And that is something that usually happens with USA companies that doesn't give a crap about EU market.
They can, there are procedures for that, as long as they pay the actual VAT rate. There are something like 8 differents standard VAT rates in the EU.