It's not that they are magically exempt, but that the error filled ones are less reproductively viable, and die out. That contrasts directly with e.g., cancer cells, that become more prolific and lead to the death of the organism.

(There's several points of 'selection' for sex cells- error free ones are, loosely speaking, more likely to successfully fertilize/get fertilized, and more likely to create viable offspring that themselves reproduce.)

Edit: It's like the difference between being able to select the top 10% and selecting those with a score above 90%. The chain gets to "select" only those that perform above a set threshold, but the organism has to play out every hand it's dealt.