When I'm accessing my site via regular (?) URL:
I can see clearly that I'm logged in.
When I'm accessing the very same Facebook Page using the very same browser (newest Firefox), without closing that browser (so session cookies are not purged), using fb.me URL:
What is this or what am I missing?
This is the weirdest thing I have ever found on Facebook. Not only my cookies are enabled (since I'm logged in, when using regular URL) — just double checked that — but also I'm able to keep myself both logged in and logged off to the same Facebook Page in two separate tabs.
Restarting Firefox brings no change it above mentioned situation.