What permission did you grant to the user.?
Even when you enable “allow users to edit values for this property” option, only users with the Manage Profile permission can edit any property value for any user.
You can find out that only three permission levels have this permission. Try to grant one of these permissions to the user, then check the effect.
Site permissions Permission
Permission: Edit Personal User Information
Description: Users can change their own user information, such as adding a picture.
Dependent permissions: Browse User Information, Open
Included in these permission levels by default : Contribute, Design, Full Control
For more information about User permissions and permission levels (SharePoint Foundation 2010), please refer to the following article: User permissions and permission levels (SharePoint Foundation 2010
When you create a web application that is not connected to an User Profile Service Application users are able to edit the information from My Settings. Default Contribute Group allows user to edit their information so everything works normally. Users are editing now in the WebApplication_Content database, table AllUsers.
In the next situation :
1) connect your above created application to a User Profile Service Application (regardless the fact no connection (e.g AD) exists)
2) create a new web application and connect it to User Profile Service Application
users can no longer edit /_layout/userdisp.aspx User Information page just because system now users UserProfile Profile DB Users and they can edit only from My Site.
The user information is controlled through your My Site profile, not the local Site Collection profile (My Settings is the local site collection profile).