Does it? Except for very sophisticated organizations, I doubt it.

You don't hear about intrusions into self-hosted source repositories. Not because there are fewer, but because they likely don't have the security infrastructure in place to know that they ever happened.

If you have private repositories that should never be public, no matter what, which isn't true for most users of private repositories, then:

Given that git provides many transports and ways to push commits around, I agree. If you have to be safe, there's no reason to use github or a self-hosted git collaboration service (gitlab, etc) on a publicly accessible server, regardless of access control measures. If you really need to have sources on a remote machine, you can limit the potential damage by only sharing archives of a certain revision, without history.

I know many will dismiss it, but if you're serious about the repositories being private, then the most you make them accessible is via an on-premises hosted gitlab instance, which is local to the company network, not accessible via the public network, and only allowed to, if you want, by dialing into VPN first. Then, to be safe, you null-route anything but the VPN traffic on the connected off-premises developer machine.

Access keys get stolen, just like SSH keys are, so you need to use a VPN service that requires additional security like the use of OTP key generators or similar measures.

This probably sounds like a hassle in the day and age of people just going for the comfort of private github or gitlab repositories, but it's what companies have been doing for almost 20 years as standard practice.

You cannot consider any git repository, even on your own root server, safe to keep private code on. CIOs would argue against that practice for good reason. The same CIOs require work laptops to encrypt all data.

If you don't need to be that serious, then an incident like this should be planned and accounted for as part of using such hosting, and shouldn't be a big deal.

We've had a couple of VPS provider admin panel compromises, Shellshock and other showstopper remote vulnerabilities for privately administered servers that don't get constant professional attention, etc. It's possible, but not obvious.

Don't you mean on-premise?