Remember that a CD player is: A transport that feeds a digital stream into a DAC, the output of which is amplified in the analog domain and available as line-level audio with a reference level of 2 volts RMS. The transport that feeds the digital stream either gets it right or not, and the DAC either deals with what it gets or it doesn't. At least since the late 90's, the DACs were functionally transparent--maybe a bit of residual distortion due to jitter, but with generally dynamic range of at least 90 dB and flat frequency response. But then there is the audio output stage, and those, I believe, have been designed with a house sound in some cases. The choice of filters affects frequency response in the top octave in some cases--my Naim CD5 (which it was working) rolled off FR at 20 KHz by a dB or so, for example.
Whether the differences are audible requires controlled subjective testing, of course. But it is not completely implausible that there would be a spectral tilt or coloration in the analog stage to give the player a characteristic sound. Even a fraction of a dB, broadly applied, is perceptible.
When used as a transport, as long as the digital stream is delivered without error, that work of converting it to audio is done by the external DAC. Some of those have a house sound, too, but not the ones usually recommended based on ASR reviews.
That said, I can't hear the difference between my many CD players, even when listening through high-resolution headphone amps and cans. I've tried, though not formally. If detecting the difference required that formal a test, then the difference is too subtle to be something I care about.
Rick "not confusing plausibility with truth" Denney