Yes, even moreso than the rest of us. The wealthy need things like corporate and financial regulation, the tort system, and other economic infrastructure that the poor aren't even aware of.
If the hypothetical wealthy citizen moves to a country without functioning government infrastructure, it's a safe bet that their first priority upon landing will be to figure out a way to move their assets into instruments that are valued in dollars or euro's.
"Yes, even moreso than the rest of us."
But, generally, the wealthy do not pay more in taxes than the non-wealthy. They generally pay less.
I like using the non-resident loophole angle. It could be possible.
The rich use more of the system than the average person. The area of law, finace, education and property. They receive money/credit for investment in local communities.
What if a US citizen obtainins citizenship in a country that does not tax non-residents, relinquishes her US citizenship and then moves to a country that has little or no taxes.