The web is so centralized at this point that I don't think Poisson processes even really apply. When Cloudflare goes down, so does half the world. When AWS sneezes, 10% of websites die for an hour. It wouldn't surprise me if Azure was experiencing some funkiness and that's what was causing GitHub's issues.
EDIT: One datapoint, Boston, MA, here still getting 500s e.g. in gist.