Sure, you can probably clone it - I'm not 100% sure, but I think laws protect that as long as it's private use.
You can also fork it on GitHub, that's something you agree to in the GitHub ToS - though I think you're not allowed to push any modifications if the license doesn't allow it?
Straight up taking the content from GitHub, uploading it to your own servers, and letting people grab a copy from there? That's redistribution, and is something that needs to be permitted by the license. It doesn't matter if it's git or something else, in the end that's just a way to host potentially copyrighted material.
Though if you have some reference on why this is not the case, I'd love to see it - but I'm not gonna take a claim that "that's very much a part of most git flows".