In reply to:
if I understand, you're suggesting that I can set up Thunderbird (Mail or whatever) on my machine to access my email without "seeing" SquirrelMail.
Yes, that was what I was pointing out. I just find that it is more convenient all around. 
In reply to:
But if, for instance, I'm using a PC in a client's office (or a Piggly Wiggly), won't I have to browse to my mail through Squirrel? [On the other hand, I may just be soooo dumb...]
Oh no, I didn't at all meant to imply or infer that you were dumb at all! And I do see your point about wanting access to your mail when you are away from you installed Thunderbird (or other email client).
I was trying to point out that there are other approaches for those situations that still let you avoid a "webmail" interface if you want to (which is what I do, because I really don't like webmail that much). I mean, when "stuck" with the occasional need to use webmail, the squirrel works "well enough" for me not to worry about installing something else, but I really very rarely use it.
Instead, I use the following approach:
1) When I am using my own laptop, I just install Thunderbird on it and set it up the same as on my "main" machine, with the exception that I leave all the messages on the server (I use pop3).
That way, I can always access my mail from anywhere I can get online, but the mail is always available on my DH mail server to be "popped" (and archived) when I get back to my "base" machine (which always *removes* mail from the server, unless I have set it to do otherwise, like in the case of an extended trip, or something).
I use the same procedure when checking my email using my Palm TC and VersaMail (that miserable thing!) 
The result is that *all* my mail is archived on my "base", and mail I get "in the field" has a copy on my laptop, or Palm, or whatever (unless I choose to delete it from that machine).
2) If I find myself using some machine I do not own (like a client's machine, a library workstation, Internet cafe, etc), and do not have access to a properly configured email client like Thunderbird, then I connect to DreamHost with SSH and use either pine or mutt from the command line to "grab" whatever I need, again leaving the mail on the server for future "popping" to my base machine like in the first instance above.
For me, that covers 99% of my remote email needs - for the remaining 1%, I just put up with the squirrel, as it is not that often, and it "does the job" well (if not very "stylishly")
There is even another approach I have used on occasion when I was using someone else's machine, if I have access to a USB port. Then, I can just carry a "thumbdrive" (or other USB drive) with a "portable" email client on it (there are several that can be setup this way, including Thunderbird) and them just plug that into a USB port, use it to grab my mail like in the first scenario above (which stores a copoy of the email on the thumbdrive, and leaves it on the server for "future" use/retrieval).
Does that make any more sense? 
--rlparker