No, just the opposite. In general, the things wealthy people buy (luxuries) experience much larger swings in demand due to price changes like added taxes (in economic terms, "the elasticity of demand"). It's because they are only wants and not needs. They are also usually easily swapped. Instead of buying your wife those diamond earrings, you could get her a painting or a trip to Spain. And rich people are often very money savvy.

It's the necessities that people will continue to buy (or at least replace with close substitutes), regardless of what happens to the price.

Obviously, in this case it worked out much differently, but no, in general you can't say the wealthy people don't respond to price changes due to their wealth.