Favorites Bug

I am using build 12.0.6504.1

We have configured permissions on the Favorites folder as follows:
- Administrators (all permissions)
- Everyone Else (only selected Standard (Private Objects) -> Full Control

What we noticed are a few bugs:

1. When a user (who is part of Everyone Else) creates a new item: he is presented with the option to create the item as Public or Private, despite the fact that seemingly he shouldn't be allowed to create the item as Public. I would have expected the OK button to be grayed out when selecting Public.
   
2. He can successfully create the item as Public and it actually appears immediately under the Favorites. Upon refreshing though it disappears and only appears to someone who has Administrator access.
   

Then I tried giving Everyone as well all permissions. When trying to modify/remove them, they kept appearing (despite the fact that I removed them and clicked OK).