We should know that this is a saved search (and we do because we highlight the correct button on the left nav bar) and show both the name and search field, and show an Update Search button if you have permissions. Otherwise we should not show the save search button at all (I think this is the case already).
Changes are on allura js/2369. To test, click on a saved search as a user with permission to edit them and as an anon user. Make sure the allowed user can save their changes, but the anon user doesn't see the controls.
Merged to dev.