People keep saying this but I can't really find much anything social about GitHub.

You can follow, star, favourite and comment on things, you get a feed where recent updates on stuff/people you've interacted are listed, you can customise your profile page with snippets about yourself, a photo, a status, contact info and add whatever else you want (including more photos, images, charts etc) in markdown. It now has discussions which are essentially a forum.

It's as much a social network/collaboration tool as it is place to store your code these days.

Some people spend most of their time in issues and PRs, which are social features mapping social interactions.

Is Bugzilla also a social network?

To the degree that it emphasizes communication between individuals over being a dumb database, yes, a bugtracker can be a social network. Bugzilla is a bit too close to the "database" side of the spectrum, whereas GitHub is at the other end; Jira sits somewhat in the middle.