According to the docs, this integration only needs read permissions to GitHub resources, and we've had it installed for a while now without problems.
However, it just requested write permissions, with no action from our end. Any ideas about what's going on?

We just rolled out some new features! https://blog.github.com/2018-05-17-new-improvements-to-slack-and-github-integration/
Doc updates are in #586
Ah ha! Thanks, @bkeepers
Should the permissions section of the README be updated to reflect the new permissions as well though?
Yes. That was the first place I went when the integration asked for updated permissions.
So a bunch of people in our organization got this e-mail a couple of hours ago:

But the link just goes to a GitHub 404 page. This seems ... messy and broken-ish.
That page has been updated, so it doesn't throw a 404, but a helpful message saying "The Slack app github is already up to date."
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Should the permissions section of the README be updated to reflect the new permissions as well though?