But isn't your "secret sauce" already on some else's servers? Like GitHub or BitBucket? What would be the exact difference here? Really and honestly interest in your thoughts. Thanks :)
No. In addition to what saurik said, setting up a full-blown GitHub-like service for your own company/institution is not that difficult.
We use Gitblit. Since it is self-contained application, it (literally) takes just a few minutes to set up [1]. After that, the number of repositories, users, and repository size is only bound to technical limitations. I get the impression that GitLab is also pretty simple to install these days with the GitLab Omnibus packages.
And even if you want to use GitHub or BitBucket for your proprietary code, adding yet another company to the loop only increases the probability that your code will be stolen in e.g. a security incident.
[1] Perhaps also important: it integrates with internal authentication servers (LDAP, etc.).
You make it sound like hosting a git repository is hard or something and so the basic assumption is that obviously anyone using git is going to be using GitHub... if you have ssh access to absolutely any server you can just do a git init --bare on the server and a git remote add on the client to let you do a git push, and with a single file rename to activate a default provided post commit hook you can turn on remote access if the folder is accessible via HTTP. You might not even need a server: the fundamental beauty of git is that it is a distributed resource. What value is GitHub adding? It would be one thing if they offered good services surrounding git (such as an issue tracker that was worth using), but they don't.
No, it is hosted on servers I own, or in a portable small repository (like Fossil, for example).
Microcomputers solved the problem of portable powerful processing, so I do not see why I would defer the processing elsewhere. It isn't a problem that needs solving.