There a 3 states you will see when when selecting the permissions of files/folders in Nautilus. 2 of them will always show. The last one will only show if you select multiple files and a condition is met. Here are the states:

Allow State (Checked) - You will typically see this state when selecting a single file. It means that that single file has allowed a Read, Write or Execute permission.

Disallowed (Unchecked) - You will typically see this state when selecting a single file. It means that that single file has disallowed a Read, Write or Execute permission.

Mixed States (Some are Checked, Some are Unchecked) - You will ONLY see this state when selecting multiple files AND (Here is the condition I mentioned earlier) the multiple files selected do not have the same permissions assigned to them. For example, In this case, some files have allowed read permission, while others have not. Some have allowed write and execute permissions while others have not. You can change this by clicking the permission box which would disallow that permission then clicking it again to allow. This will affect all files selected (Assuming you are the owner). This state only shows when there are mixed allowed/disallowed states but this can only happen if you select multiple files/folders.

UPDATE: With the added image that shows Folder and File permissions and with several tests I did on my PC I can say the following:

1. The Nautilus File Properties are not being read correctly when selecting the parent folder. They will always by default show as Mixed.




2. You can change the permissions to all files and folders inside a parent folder (Which would change the permissions to all files/folders inside if you click on Apply to enclosed) but they would still show as mixed if you select the permission properties of the parent folder again.




3. Changing the file permissions in the Parent folder does change the permissions of the files/folders but again, it does not correctly detect them.

What you have found in that particular part of Nautilus is a behaviour I find more related to a bug than to a normal way of operating. I should mention, this also affects the normal visual way (Default) of showing the Permissions, the file permissions are again, not shown by default, even if all permissions are the same for all the child elements.

I have found several bugs indicating this is an old behaviour (Or related to it):

https://bugs.launchpad.net/ubuntu/+source/nautilus/+bug/503315

https://bugs.launchpad.net/ubuntu/+source/nautilus/+bug/822993

https://bugs.launchpad.net/ubuntu/+source/nautilus/+bug/94512

There might be others, that is just a quick look I did. In any case, I recommend creating a bug report or following one that exists related to this one. Note that it affects the visual way of changing permissions and your tweaked way of changing permissions (Apart from confusing the heck out of old and new users).

Hope this answers your doubts because it sure helped me figure this problem out.