Ok, I got my problem figured out.
The problem was with my use of basic authentication being used to protect the site I'm currently testing with Squid acting as a HTTP accelerator.
Once I added a "public" Cache-Control header to the mix, everything started working just fine AND with Squid 3.0-STABLE12.
The only thing is with Squid 3, you will get these warning messages in the cache.log file:
2009/01/24 17:46:54| ACL::checklistMatches WARNING: 'cookie_logged_in_set' ACL is used but there is no HTTP reply -- not matching.
2009/01/24 17:46:54| ACL::checklistMatches WARNING: 'cookie_logged_in_out' ACL is used but there is no HTTP reply -- not matching.
This is due to the use of the rep_header ACL acltype being used. Apparently, at the time that ACL is processed, the request to the origin server hasn't been made yet so there won't be any HTTP reply to process:
In any event, things seem to be working just fine now!