I have a site using CB where users must maintain their own details but not have access to other profiles. I've enabled Core Fields Ajax to assist with this. It works fine when user is an admin, but not otherwise. I traced this behaviour to the setting in Configuration>User Profile>Profile View Access Level - it works perfectly if the setting is a user group to which the user belongs. If not, the pencil icons appear but clicking on the field causes the entry to disappear, and no editable field or Update/Cancel buttons show.
Is that expected? It seems odd because the user is still able to access cb-profile-edit via menu, just not directly via the Ajax plugin. If so I won't be able to use the plugin as I need to set the Profile View Access Level to admin-only.