Your guess is wrong as Firefox doesn't use GitHub for any of that, and AFAIK there are no plans to either.
The blog post linked in the top comment goes in to this in some detail, but in brief: git log, clone, diff, showing files, blame, etc. is CPU expensive. You can see this locally on large repo if you try something like "git log path/to/dir".
Add to this all the standard requirements of running any server that needs to be 1) fast, and 2) highly available.
And why bother when there's a free service available for you?
