OK, I did some more checking. Sometimes Amazon includes a “note” on their sales tax, and sometimes not. And in the note, it explicitly states that they are going to check, that the sales tax they show may not be right, but that the correct sales tax will be charged to your card.
Under those circumstances, how could any customer think they have to do their own sales tax?
Some online retailers already collect taxes in VA, like Underarmour, Nike, and Neiman’s.