People who think it's high taxes which cause people to flee high cost state, they are ideologically blinded, naive fools. High taxes are a part of the reason but it's rent which really impacts people. Only rich people have the luxury to worry about tax rates.
Rent is partially fueled by property taxes.
Cite?
Perhaps large apartment complexes owned by property management companies factor property tax into rent increases, but most normal people aren't that calculated in their decisions. I've had landlords raise the rent with every lease renewal proposal arbitrarily, regardless of whether their cost of ownership increased or decreased. Simply asking for a reason gave me my old rate back. It's just too tempting to try and take an extra $10 a month.
As memphis said, it's also basic "going rate" supply and demand. Property owners are no more or less sheep than the renters.