Yes but, like everything in economics, the only people who really suffer from economic policy are those with the lowest (disposable) income. If you don't have a mortgage, or any other type of loan, then rising interest rates make no difference to you. On the contrary, if you have substantial savings, then they are of huge benefit to you!
It's similar to the negative equity that used to be everywhere in the late 80s / early 90s. Negative equity makes it difficult to sell your house but, if you don't want to sell your house, it makes no difference whatsoever to you, so long as you can afford the monthly mortgage payments.
Of course, it's easy to say that raising interest rates means that the rich get richer and the poor get poorer. That's true to a certain extent...