"I bet in other contexts (say insider trading), you'd agree that it doesn't matter whether some CEO tipped off his buddy about insider information by carefully varying load on a server to modulate response times on a web page, thus communicating bits of information."
Ah, but what if the CEO is just taking a long time to reply to emails from friends, because he is very busy preparing for some huge business move -- is it insider trading if one of those friends sets up an options position that profits from increased volatility? This gets down to the difference between a side channel (inadvertent) and a covert channel (deliberate). The distinction does not matter from an information theoretic point of view; the same information is communicated in either case.
Ah, but what if the CEO is just taking a long time to reply to emails from friends, because he is very busy preparing for some huge business move -- is it insider trading if one of those friends sets up an options position that profits from increased volatility? This gets down to the difference between a side channel (inadvertent) and a covert channel (deliberate). The distinction does not matter from an information theoretic point of view; the same information is communicated in either case.