Yes,
You will pay the California state-wide rate if you pick up at the factory. (You should not be assessed the local rate for Alameda County/City of Fremont.)
When you register your vehicle in Minnesota, the state should give you credit for "sales tax paid to another state." Since the Minnesota rate is lower than California, you will not owe anything additional to Minnesota, but you will not receive a refund, either.
I know it sucks. But California is not the only state to cast such a wide net.
I think one must look at this from the State's point of view. You could have all sorts of proof of Minnesota residency, yet you just completed a move to California or recently became domiciled in California (there is a difference.) Or, you could be one of those larcenous types who tries to game the tax system. (No accusation, just trying to view things from the other perspective.)