Thanks for your response.
Is this also standard behavior?
When at the site collection home level, the user navigates to their profile page via the top right ribbon user menu ([name] > My Settings). Above the table of user data they see a menu that reads 'Edit Item, My Regional Settings and My Alerts'.
When not at the site collection home level, i.e. a child site, and they access their profile using the same method, the menu doesn't appear.
When the user clicks 'Edit Item' they can edit the profile information but when they press save it gives them an access denied page. Appearing like they can edit their profile but when in reality they cannot.
If this is standard behavior then perhaps this 'Edit Item' link should be removed from the userdisp.aspx by default at the site collection level.