If you use tor or use a public WiFi service then you'll be much more hidden.
Public WiFi is not secure, anonymity in this regard would be better with Tor.
And cameras, do not forget about cameras.
For example : if you go to bar/cafeteria to use their free WIFI, the most probably you will be recorded.
I think it's similar to having a gun - it gives you a false sense of security (in this case, anonymity).