Sure I mean I can't give you a source per se but I think anyone that has been using github for a few years is familiar with the "forking" model( evidenced here with github giving steps for how to synchronize your forks - https://help.github.com/articles/syncing-a-fork/)

Branching is a separate concept and its certainly accounted for in the forking model. But we are talking about the process driven meta layer that github has stacked on top of git. Their original proposed workflow did not have a bunch of folks working out of the same shared repo instead(and this even extends to their enterprise model) every user that start working on a project would fork it. You'd make your changes and contribute them back to the authoritative repo as a "Pull Request". Branches model an evolutionary line of code, but a "Pull Request" models a change that you want to introduce typically into another repository. The implication here is that forks and branches are separate concepts that share some overlap. I often branch in my fork and contribute my change from my forked branch to be introduced into `master` in the authoritative repo without ever delivering the branch itself. Rather simply merging the changes into `master` as a discrete unit of work. Github's polite suggestion that you work this way is further evidenced by encouraging you to delete merged branches. I find this to be satisfactory but many people have personal hangups with deleting branches for reasons that are not entirely clear to me. This model allows me to sync my fork's version of "master" periodically with master in the repository of record(typically referred to as "upstream") and bring those changes into my branched work.

"Forks" and "Pull Requests" are not git concepts they are github concepts. Forking provided a nice little metaphor for locking down a repo because you couldn't create a disaster for anyone but yourself. Many git saavy organizations do not allow direct access to the authoritative repo instead only allowing "Pull only" access. This allows the authoritative repo to pull the changes that add value and reject those that do not without adding lots of cruft. This harkens the "Social Coding" aspect that github wanted to develop in their earlier days. With everyone contributing to everything forking left and right. Businesses wanted to piggy back of the toolchain they created but most folks weren't familiar with the idea of social coding and/or had needs that weren't addressed well by the social coding model. Github said no worries I think I can tailor this to a business. Which is why you have lots of fork based tools for private repos( organizations can take ownership of private forks, can force forks to be private, can set organizational ACLs on forks and private repos, etc, etc)

Some not so git/github saavy organizations work out of a shared repo for reasons that aren't very clear to me. Its usually a misinterpretation of who owns forks and/or the visibility of private code. I get a sense that github fought these ideas for a long time just saying "c'mon friends just use forks" and that this is their aim at a compromise.

>branches are the "git way," no?

This takes us to this. The answer is sort of. Really cloning is the git way. You clone a repo and synchronize it with other people's repos. Most organizations realize pretty quickly that some repo has to be the repository of record, but git doesn't care. To it a repo is a repo and you know what you are doing. Github just layers a little process on top of the "git way" turning a "clone" into a "fork" and add a little ceremony to the contribution process.