It seems as though there are two principal attacks on the idea that interconnects make a difference:
1) The lack of sufficient evidence via double-blind, controlled experiments, etc., and in the absence of such, that it's possible to fool ourselves psychologically/psychoacoustically
2) The absence of an explanation for any improvements using currently accepted scientific theories.
The problem is that equally, there don't appear to be a plethora of proper controlled experiments to utterly rubbish the claims, and just because currently scientific theories can't account for an effect, doesn't mean it doesn't exist. It's entirely possible that our scientific understanding needs to be extended.
Neither side has sufficient compelling evidence to win the argument. The cable-o-phobes bang on about how the case is not proven, the cable-o-philes point out that it isn't disproven either. We might as well debate whether God exists. Since none of us seem to be in a position to provide proper peer-reviewed research, we are left with discussing and exchanging our ideas and experiences, which I contend is a more productive and rewarding activity than the automatic gainsaying of what the other party says.
If you doubt that subtle and counter-intuitive factors can have their effect, a lot of folk in audio production leverage it to great effect and are forever experimenting to that end. Who would have thought that adding a little bit of low-level noise to a signal might actually enhance your ability to perceive detail? Or that distortion might actually in some cases wind up sounding "better"? Initially some people hear the effect, later some find a way to explain it. The same could turn out to be true with cabling. Similarly, it is entirely possible for some to notice effects more readily than others, painful as it may be for some to accept.
To get an idea of what audio engineers have to deal with in this regard, check out this interview transcript with audio veteran Rupert Neve, the salient part coming quite early on (the bit about Geoff Emerick)...
http://www.prosoundweb.com/chat_psw/transcripts/rupert.shtml
... not that I mean to open up another area of contention...