You are right. When a state has a sales tax, it also has a use tax, which requires that if an item is purchased out of state and brought home, the purchaser is supposed to pay the difference of the tax paid (if any) out of state and the local rate of sales tax. However, for individuals this is basically impossible to enforce. The State of Utah does audit some businesses as assess use tax on item that they purchase over the Internet.  

The problem for states stems from a 1992 US Supreme Court case, Quill Corp. v. Heitkamp. http://markbarnes.us/Sales%20Tax%20on%20Internet%20Sales.htm In Quill, the Court held that a state cannot require a business with no physical presence in that state to collect its sales tax from residents of the state. This case involved catalogues, but also applies to the Internet. The Court reasoned that such a requirement placed an undue burden on interstate commerce and thus violated the "dormant commerce clause" doctrine.  

This was actually an improvement for the states over the 1984 case of National Bellas Hess (http://caselaw.lp.findlaw.com/scripts/getcase.pl?navby=case&court=us&vol=386&page=753 ), which held that such a requirement was a violation of the due process clause of the 14th Amendment. This finding would require a constitutional amendment before the states could require collection of their sales tax. Quill only required an act of Congress, since it is up to Congress to regulate interstate commerce under the commerce clause.  

National Bellas Hess logically followed the “minimum contacts” test of another famous case, World Wide Volkswagen, http://markbarnes.us/World-Wide%20Volkswagen.htm. World Wide Volkswagen said that a state court cannot assert jurisdiction over a defendant, if the defendant does not have some significant connection with the state. In that case the defendants were in the business of selling cars in New York and had no contact of any consequence with Oklahoma. The Supreme Court held that before a state can assert jurisdiction over a defendant pursuant to the due process clause of the 14^th Amendment, the defendant must have “certain minimum contacts” with the state.  

Note that taxation, like jurisdiction, is an assertion of state power over a person. Thus, taxation and jurisdiction cases follow similar test. By 1992, the Court dropped the due process argument, because it is clear that a person can have significant contact with a state without ever being in the state. Amazon.com has significant contact with Utah through it Internet sales, without ever being in Utah. Thus, by 1992, the only real issue remaining was the commerce clause issue.

However, since the Quill decision in 1992, Congress has declined to enact legislation that would require businesses without a physical presence in a state to collect sales tax. On the one hand, this shows Congress' desire to promote Internet business with an indirect subsidy (be it at the expense of state governments). On the other hand, it results in a rather strange system in which a book ordered from Amazon.com is not taxed (no physical presence), while a book ordered online from Barnes & Noble is taxed because they have a physical presence in the state.