Resolution: Won't Fix
We use scripts to talk to Jenkins to administrate it. The scripts use a non-GitHub account (using the built-in User store in Jenkins). An example of this is the Jenkins Cookbook.
These scripts broke with github-oauth-plugin v0.26 because these users don't have GitHub accounts.
I know you just fixed all this, sag47 and I really appreciate your hard work on it.
I think what I would expect is that if someone used an SSH key or the API token that it falls back to the old behavior of not being in the github organizations.
I realize this is a little confusing for users; I can't think of any alternate ways to allow both GitHub users and non-GitHub users to work together.