Let's put this another way. Data programs are not time sensitive when they install. The CD drive can re-read the disk as many times as it wants. If the disk is in good shape, it reads the disk perfectly at 50X (or whatever.) If the disk is in poor shape, it tries until it gets it right. If it never gets it right, you get an error message that the program can't install correctly.
When you rip a CD on a computer, the drive has a similar opportunity for multiple reads within the confines of Reed Solomon. If an audio CD does not need to be re-read, it rips quickly. If the drive is having trouble getting an accurate read in an error correction mode, it reads slowly. Slow ripping does not improve error correction if no errors are popping up.
When a regular audio player plays a disk in real time, it has to read it at 1X and get it the best it can the first try. If it has to re-read a section of the disk it can't deliver the music in real time, so audio players typically don't re-read. They may interpolate to fill in the error with a "guess" about the music that should have been there.
Players like the memory player are more like a computer drive. They stream the data into a memory buffer and the actual 1X output is sent to the DAC from the memory, not the CD itself.
However, with your last sentence you introduced a variable that hadn't been on the table in the earlier discussions. You indicated you want to "burn a copy." An original CD is encoded using pits and lands that are pressed into the CD. A CDR is layered with a special coating that creates the binary code by burning the appropriate areas with a laser, which then become non-reflective.
It can be argued that some stand-alone players read a commercially produced CD differently than a CDR. (Some audiophiles claim that CDRs are generally superior to CDs.) However, anytime you're playing something in real time, jitter becomes an issue. Jitter is a function of timing precision in the decoding from digital to analog. It is not an issue when you're only talking about accurate data transfer during the ripping process.
So two different issues at work. Ripping is a data transfer function. Playback (from whatever source) is a different can of worms.