Checking my logs more closely, it appears that each time an RSS file from my site is loaded by one of these applications, a referer is deposited in the log file. Each time I load a page in Internet Explorer, I don't leave a referer for www.microsoft.com/ie in the log files of the site whose page I loaded, so why should any of the RSS readers be different?
To answer the question - the readers shouldn't be different, and in fact at least two of them are not. Both Amphetadesk and Aggie allow the user to specify the referer -- which is the only proper thing to do. In this way the referer gives information about who is doing the browsing, rather than what web page they were referred from, which unfortunately isn't kept track of.