This can easily be manipulated - people are literally writing scripts to do regular but random commits to private repos.

I feel like companies don't use Github as much as individuals. I've seen Azure DevOps used a lot, Gitlab right behind that, Bitbucket as a third option, however I've yet to work for company using Github organizations. And I don't blame them tbh, Github for organizations, has less feafures, but costs a ton more than other alternatives. Other thing i've notices is that sometimes, bigger companies have special deals with Microsoft, that for example include some Azure DevOps features for free.

Do the non-programming vice presidents at these companies know that you don't need a 3rd party host to use Git? That literally a networked file share is enough (assuming a decent VPN)?

Oh, what am I saying, they're mid-level management. Of course a bloated paid solution involving a 3rd party vendor wins over simplicity. Otherwise they'd be out of jobs!

Some of the hosts have significant added value. (And you can self-host them.)

I know of at least three huge, multi-national corporations using Github extensively - either via separate, protected orgs and repos directly on github.com, or a separate Github Enterprise instances on their own domains.

The commenter you're replying to can chime in here for an accurate response- but I assume what he's referring to is that a company usually assigns you a fresh, internal GH account. My past three jobs have all done this, which makes it even harder to demonstrate the work I've been doing to employers... Especially when after leaving a company my GH profile is terminated.