Original comment by @marius-dr:

The Edit and Status page should be unavailable to the user for the cluster alerts watches. This is true for the Edit page, but the status page can be accessed by using the direct URL to it like this:
Cluster alert watch ID: lgifRU4RTCKjZ-7391mVIQ_elasticsearch_cluster_status
URL: http://localhost:5601/app/kibana#/management/elasticsearch/watcher/watches/watch/lgifRU4RTCKjZ-7391mVIQ_elasticsearch_cluster_status/status?_g=()

You can Activate/Deactivate and even Delete the watch from that page. If you click on the Edit tab, it will show a blank page, so that one is safe from tampering.
We should should block access to this page as well and maybe add a message on it.