Using the generic webhook trigger plugin myself, while still relying on OpenShift authentication logging into Jenkins, I don't remember having anything like this.
Although I can't explain why your plugin would refuse this, unless maybe something's wrong in Jenkins permissions matrix?
As far as I've seen, generic triggers from a BuildConfig wouldn't allow for multi-branch jobs - or if they do, I'm still looking for a way to retrieve the triggering branch as a variable somewhere (note: that ruddra sample shows the buildconfig has a "ref: master", which would suggest it is not multi-branch capable).
So far, Jenkins plugins was my next best solution, although not ideal.
Anyway, you might be able to create a role - or clusterrole - and corresponding binding, with something like this (not tested)
- nonResourceURLs: [ "/bitbucket-scmsource-hook/*" ]
verbs: [ "get", "post" ]