Tbg - dunno how many or which players invert polarity. I dunno why either, but I don't think they do it on purpose. Maybe they are like recording engineers and just donl;t think about it.
There are three reasons why a consumer audio product would invert phase:
1. Ambiguous or no standardization on hookup of balanced interconnections (i.e. the XLR pinout conventions that Atmasphere mentioned)
2. Error in design, manufacturing, or nomenclature
3. Preference for circuit design topologies/combinations for which inversion is a side-effect. An example would be a two-tube line preamp where the first stage is a plate-loaded voltage amp, and the second is a cathode follower . . . the signal will come out inverted, unless another stage is added to flip it back around. These types of circuit designs are increasingly eccentric and anachronistic in modern equipment . . . and pretty unusual even in the field of enthusiast audio where eccentricity and anachronism is widely respected.
Reason #3 is especially uncommon in CD players and DACs, given that the overwhelming majority of high-quality DAC chips have balanced current outputs and/or on-chip signal inversion capability . . . meaning that the designer can just as easily preserve signal polarity regardless of the design of the output stage. That's why I used a CD played from a Pro Tools recording/mastering process as my "good bet" example.