There is no way to suppress client side tools to inspect the HTTP communication between the browser and the server. Even HTTPS doesn't help here, as browser integrated devtools have access to the decrypted information.
Also, as mentioned when I was on google, facebook firebug simply said
Access Denied.
As you didn't post any info about where you saw that message, I can't tell you the reason why you saw it. Though the server needs to expose certain info to the browser, so it can interpret the request correctly. And there is no means from the server side to forbid the client to read that data - even not pages like Google or facebook as you can see in the following screenshot.
