No, see - that's the problem. The vast majority of the electorate has no idea either that our system is broken or that other countries actually do things better - indeed, that it is even possible, in principle, to do anything better than current practice in the United States.
They think that if we don't have the expensive, privately-held bureaucratic system we do, then GE can't charge what it does for its MRI and CT scanner machines and exit the market, and then Grandma will die a horrible, painful death in a ditch outside Waukegan. Or, if pharmaceuticals don't charge insured patients $10000 a dose of some new drug, that our system will collapse because no one will make medicine in America ever again (never mind that 5 of the top 10 largest drug makers are outside of the US in countries that have abundantly socialist healthcare systems).
That is, if there is some structural pricing advantage in the U.S., what is stopping those companies from benefiting from it?
If the companies do (significant) business in the U.S., then the mere existence of those companies isn't useful evidence against the fear "that our system will collapse because no one will make medicine in America ever again". The specifics of where the pharma companies are getting their research dollars are more interesting than the specifics of their incorporation.
(but I don't personally fear that research funding would go away, and I accept that those companies have huge revenues outside the U.S., etc.)