Incorrect, closing cards changes your credit timeline (how long you've had credit) which will not recover for years. It will also immediately reduce your debt to credit ratio, which will never improve unless you get more cards, or greatly increase the limits on your remaining cards.
Edit: It will also reduce the number of active accounts you show which is another of the five factors of credit worthiness for personal credit. Closing cards hurts your credit in every way, and does nothing to help you. The one exception is if you are poor at managing credit, it can be safer to just not have it available.
Finally, interest rate doesn't matter IF you can pay off the bills every month. That's all part of actively managing your credit though, and not everyone feels the need to do so.
Like many things, how you manage your financial life is up to you, but I don't want you to make decisions based on false information.