As in most populist programs and journals the facts are irretrievably dumbed down.
All analogue to digital and digital to analogue processing processing is imperfect however, within the limits set by recorded music, and with good modern equipment these imperfections are way beyond audibility. Multiple passes are not an issue either, this was demonstrated with multiple PCMF1s back in the early 80s. Modern equipment is much, much better.
In addition to simple A to D and D to A conversion digital processing equipment also carry out such functions as sample rate conversions, format changes, WAV to FLAC for instance, and of course the 'ripping' of the CD datastream to your preferred format. Once again these processors are imperfect, they do not all produce identical results but once again any differences should be way beyond audibility.
Once a recording has been 'ripped' to a digital file, that file can be copied, ad infinitum, with absolutely no loss of quality. As pointed out, computers simply would not work if this was not the case.
With regard to data reduced encoding, results from the better codecs at reasonable bitrates (256-320kps) are extreemly close to the full data file, so close that most people, most of the time can not hear the difference. In this case the differences are easily measured so they are present and under some circumstance can probably be heard.
This of course is a subjective evaluation, so will differ from person to person, though most hi-fi enthusiasts, many of whom insist the difference is huge, are unable to distinquish one from the other in blind tests.