Yep. Millionaires threaten to move away if they're taxed, but they won't. The convenience of having their high value properties in highly sought after areas, where all the services they use are present, is too enticing, and even a hefty tax won't be a deterrent.
Just imagine how much upheaval it would cause you to move a few states over. For a millionaire... it's the same except they're used to so much beyond basic survival - their parties, their exclusive clubs, exclusive gatherings, private boxes in theatres, the list goes on.
Do you really see such a person moving to Bumfuck Nowhere, Nebraska, just because that town doesn't tax millionaires? Do you really see them giving up 80-90% of the "rich life" just to save their wealth? Hell nah. As long as you're not explicitly threatening to tax them out of existence, they'll stay. Because unlike the average people they can afford that extra expense.
But of course they don't want to, they just yap around threatening the move without committing to it.