Do any of these "other means" involve installing shady software on people's computers?
They've had many opportunities to do stuff like that with their iOS and Android apps but have never dared.
My point is they wouldnt need to install shady software on your machine. They're able to track you with their like button.
I find it amazing that people seemingly don't know that Facebook tracks you across the web through those embedded Like buttons, and more amazing that many who do know don't seem to care.
There's a reason I have the equivalent of "127.0.0.1 facebook.com" in my /etc/hosts file.