I think Amazon is desperate. It used the advantage of tax free to hurt many retailers. Because of this many retailers like CompUSA and Circuit City were forced to close. Amazon was not sued by the courts.
Amazon's "tax-free" advantage is drying up. It wasn't precisely that, and it didn't start with internet sales. I can't remember the name, but there was a specific case with mail order catalog companies involving the ability of a state to mandate sales tax collection across state lines. The states responded by placing a "use tax" in lieu of sales tax on items that were either purchased from an out of state vendor or shipped out of state to an alternate address to avoid sales tax. Typically if you order from out of state or purchase something above a certain amount to be brought back to your home state within whatever state set number of days, you owe use tax through a filing with whatever agency deals with that in your state. States don't have the resources to pursue everyone who doesn't pay, and this has become more prevalent in the internet age, so they start to bicker with retailers instead. Amazon doesn't seem to be totally against sales tax across state lines, as long as others are also held to that. I would still order things off Amazon for the convenience factor. Right now consumers often treat it as a price advantage, and it does hurt brick and mortar businesses to a degree.
I'll add that the sales tax issue wasn't the only reason those stores experienced difficulties.