When the CD is badly pitted (CD Rot) then the data can no longer be reconstructed using error correction and the player often interpolates between one data point and another.I think you're getting the concepts of mathematical interpolation, "interpolation" as used in digital audio oversampling, and error-correction confused.
Mathematical interpolation is the process of deriving an in-between point from two outers. It's very processing-intensive, and quite uncommon in real-time audio DSP and data error-correction systems.
"Interpolation" in oversampling digital filters is an approximate term, usually used to describe the a combination of zero-stuffing unknown samples, and then low-pass filtering the output. It's used for its processing efficiency, and because it creates a very predictable noise spectrum, which can then be filtered out.
Error tolerance in CD transports is goverened by a number of factors, from the ability to keep the motor PLL locked, to the timing characteristics of the focus and tracking servos, the noise and accuracy of the EFM preamp and demodulator, etc. . . . and finally, "error correction" in the form of redundancy and parity in the data, through its modulation and coding characteristics. All of this happens ahead of any processing of the linear PCM data.
It is true that when data is truly gone . . . it's gone. But subtle differences in the design of the optical drive reading the disc have a huge impact on its ability to tolerate different kinds of errors, and a computer CD-ROM drive reading at high speed definately has a very different perspective on disc errors than an audio CD transport reading in real time. And if one was to design software that reads error-strewn areas of the disc many, many times, then a huge advantage can gained by averaging out noise, which enables the redundancy and parity mechansims in the EFM and Reed-Soloman techniques to work more effectively.
In short, if you get a clean rip from the CD into your computer . . . you really are getting more data off of the disc, and you shouldn't worry about whether or not you're then listening to "fake" or "interpolated" audio.