Fuzzy means that it takes compression and the like into account, because even if just one pixel out of 20 thousand is different, the hash is different too. Fuzzy hash still recognizes it as the same image, so using an algorithm to alter the color etc. won't work.
That's also true for the no-fly list and the Terrorist Screening Database,[1] yet those are full of false positives. And unlike those lists, CSAM databases cannot be independently verified. To do so would require having the original images, which is illegal.
1. https://en.wikipedia.org/wiki/Terrorist_Screening_Database
So if you're charged on the basis of a fuzzy hash matching, you'd subpoena Apple for the photo in your backup that matched, present it to the court (since it doesn't actually matter if it's CP or not to be admissible), and you win the case.
0. https://www.johntfloyd.com/the-difficulty-with-criminal-evid...