Right, and before this decision, it was that person's responsibility to remit. Now it is the business's. So the burden of remittance has shifted to the disenfranchised party.
And the party paying the tax has not shifted. The party paying the tax votes on representation.
Technically the business is "the party paying the tax", in the sense that they are the party sending money to the government. If I drop ten dollars on the counter and sprint out of a store carrying an item that costs ten dollars plus tax, the store is still responsible for paying tax on that item to the government.
The laws of various states place many restrictions and requirements on businesses who want to sell to their citizens. This is just another one of those.
[x] Taxation
[ ] Representation
I'm not a fan of the ruling but I would expect the answer to your question would be: "No because you aren't forced to buy the product from a retailer in that state"