It is propable as designed.
Dynamic properties are considered as global and not page specific since their values are inherited by all pages below where the property is set.
If you upload files in this "0" folder and get access denied problems for visitors it is another issue that should be reported as a defect to support.
One of my sites has an XHTML dynamic property. When using the editor icon to insert an image, the file explorer pops up with the "create folder now?" dialog. If I choose to create the folder, the page file folder name will permanently be set to "0". It should have been set to the name of the page I was editing?
Why is this, and how do I change the page folder name?