Ahh. Makes sense then - I wonder if GitHub allows granular permissions from OAuth requests?

Looks like they don't, unfortunately - https://developer.github.com/v3/oauth/#scopes

They do. From the link you provided:

public_repo - Grants read/write access to code, commit statuses, collaborators, and deployment statuses for public repositories and organizations. Also required for starring public repositories.

repo - Grants read/write access to code, commit statuses, collaborators, and deployment statuses for public and private repositories and organizations.

Also, I don't think they need write access at all to your repositories, so I think the default no scope would be sufficient

(no scope) - Grants read-only access to public information (includes public user profile info, public repository info, and gists)

Well, by granular I meant on a per-repository basis, ie. so you could grant an application access to only one repo (If anyone from GitHub is reading this...)

As RadioactiveMan said, they have a somewhat undocumented feature where they will sync your screep code with a GitHub repository. The only way to do that with GitHub scopes is to allow full read/write access to your all of your repositories including organizational repos.