Because Amazon leaking your email address means you are registered on Amazon; there is a high likelihood that you actually purchased stuff there, and therefore they have your address on file, and maybe even your credit card.

Since a lot of people re-use passwords, if your email is also contained in one of the countless breaches that we've seen cropping out in the last few years, there's a good chance that your Amazon account is using one of the pwned passwords: therefore Amazon's statement that people should not change their Amazon password is potentially harmful advice.