One more note: I'm not using any other extensions at this point. Also,
it ONLY happens when the Firebug Net panel is enabled. Enabling or
disabling any other panels does not have any effect. The login menu at
the top of the page makes it easy to switch between being logged in
and logged off (it remembers your recent logins) which makes it easy
for testing.
When the Net panel is enabled, and I switch between users (and the
backend db says it is changed), I notice that the Net panel does not
show the main page HTML file which I think is at the heart of the
issue. It is pulling from cache, not reloading.