I believe the interstate commerce laws prevent states from charging you sales tax in a 2nd state for something you bought in another state. But they can charge you extra if the sales tax is higher in the 2nd state or ding you again for fees you paid in another state.
I ran into that when I moved to Washington and went to register my car bought in California. They wanted proof of the sales tax I paid in California, but I didn't have the documentation for it, so they were going to charge me Washington sales tax because I couldn't prove I had ever paid sales tax on the car. After going a few rounds with them, they agreed that I couldn't have registered the car in California without having at least paid state sales tax (they wouldn't accept local, even though I had proof where the car was registered before and at that time the local sales tax was the same in every county in CA). So they calculated the CA state sales tax on the amount I paid for the car at 4.5% and then calculated the current value at the 8% rate currently being charged in my part of King County, but they depreciated the car to the current Kelly Blue Book value which came in just under the 4.5% of the original sales price. So I just made it and didn't have to pay Washington sales tax to transfer the title. They did ding me for everything else they could think of though.
This was in the late 80s and the car registration fees are very different in Washington today, but I believe the sales tax thing is still valid.
For people who live in states like Oregon with no sales tax, or states with lower sales tax rates than California (most state these days), picking up at the factory is a bad deal because you will be paying California tax instead of your state tax. However, I don't know if picking up at the factory has any other registration fees like a CA temporary transportation permit, or a temporary registration. You could get dinged twice for those going back to your home state.
I thought about picking up at the factory but the sales tax difference was about $1000 more.