Step 3 of this activity:
https://github.com/foss2serve/github-workflow-activity/tree/master/activity
Leads to step 8 of the following activity:
https://github.com/foss2serve/github-workflow-activity/blob/master/activity/create-an-organization-and-a-repository.md
I think the rules have changed on Github and now when the user accepts an invitation the users get "push" access to the repository.