Wow... this is a strange one. I'll have to admit I spent "way" more time doinking about with this trying to figure out what is happening than I wanted to, or should have had to, because the more I looked at it the more infuriating it became because of the inconsistencies.
To see what I mean, check out these urls in FF and IE7:
[color=#CC0000]The icon is displayed in both FF and IE[/color]
Server: Apache/1.3.37 (Unix) mod_throttle/3.1.2 DAV/1.0.3 mod_fastcgi/2.4.2 mod_gzip/126.96.36.199a PHP/4.4.8 mod_ssl/2.8.22 OpenSSL/0.9.7e
Last-Modified: Wed, 16 Apr 2008 11:25:50 GMT
[color=#CC0000]The icon is displayed in FF but is NOT displayed in iE7[/color]
Server: Apache/2.0.61 (Unix) PHP/4.4.7 mod_ssl/2.0.61 OpenSSL/0.9.7e mod_fastcgi/2.4.2 DAV/2 SVN/1.4.2
Last-Modified: Tue, 15 Apr 2008 02:21:36 GMT
[color=#CC0000]FF offers to download/save, but IE7 displays the icon[/color]
Server: Apache/1.3.37 (Unix)
Keep-Alive: timeout=15, max=59
Just for giggles, I went and added the Content-Type: image/vnd.microsoft.icon to my server's mime types on maddogz.com (per the information on http://wiki.dreamhost.com/MIME_Types) and anybody want to guess what happened? When visiting the first link above, FF displayed the icon fine, but IE7 refused to display it.
As silly as it sounds, it actually looks to me that the most problematic arrangement is IE7 being served the image/vnd.microsoft.icon mime type ... go figure.
There may be different mime types registered on different DH servers, (we don't have sufficient permissions to read the mime.types files, and I don't know if the wiki article referenced above is authoritative, current, or true for all the servers) so it may take a support request to find out exactly what is installed on your server.
That said, if YOU added that image/vnd.microsoft.icon mime type via an AddType directive in your .htaccess file, you can probably get things working as you expect them to by removing it. If, however, DH has that in your server's mime.types file , you can try "over-riding" it by placing:
AddType image/x-icon ico
in an .htaccess file in your home directory (or even in the directory with your .ico files); it might give you a workaround for the IE borkedness.
sigh... why is it that everything Micro$oft "does" on the web (the ".ico dance" being one example!) is inherently farked-up at birth? ARGUGGGH! Interesting reading to be found at http://en.wikipedia.org/wiki/Favicon