What is the index name that you are using in your set processor?
I'm not sure, but I think that if the name is not one of the default names, like logs-* or metrics-* it will not work.
Check this similar question.
The documentation is a little confusing here, as it gives the impression that you could change the permissions for the elastic/fleet-server, but I don't think this is possible, it looks like this was a poor choice for an example.
@TimV Sorry to tag you, but since you answered a similar question, can you provide a little feedback here?