A lot of CDs aren't in perfect condition, either because of scratches or things like https://en.m.wikipedia.org/wiki/Compact_disc_bronzing. When faced with damaged data, the quality of the drive and its firmware will influence whether the data stream corresponds to the original content or not.

Thanks for the explanation - I misinterpreted the OC to be about audio quality rather than just trying to recover data from damaged media.

Given a perfect CD the drive is probably not going to have significant impact, but for an audio CD that's been exposed to real world conditions there's a bunch of ways the drive can make a difference to the recovered data.