Jeremy - You're right about what cables are supposed to do. Everything else, except that you thought you heard a difference, is either questionable or false.
Simply stated, the limit to what the human ear can hear is very near to the threshold of pressure caused by Brownian motion in the air. Our ears are amazing equipment. As good as ears are, instrumentation can measure differences that are orders of magnitude smaller.
It is common for anyone to hear, smell, taste etc. differences where they do not exist due to expectation. This is simply part of the human condition and should not be taken as a defect of any kind. Rather it is part of what makes life worthwhile. I can walk outside and be sure this is the prettiest sunset I've ever seen without comparing a library of photos.
In contrast to some more complex items, cable properties are easily measured and quantified. Thus it is trivial to show that a reasonably constructed cable will present for all audible purposes the exact same signal at both ends, therefore being perfectly 'transparent' to the electrons involved. Any audible difference from this is going to be (1) measurable and (2) distortion.
Ever wonder why the agencies with the most to gain (cable manufacturers) are the most reluctant to participate in double blind or ABX cable tests? If their claims are true, they could prove it scientifically and reap the windfall. But they, to an man, steadfastly oppose any sort of repeatable blind tests. Why is that I wonder?
The have started their own religion and are busy reaping tithes from the faithful.