Access Denied: Enabling Permissions Inheritance

I'm having trouble with file permissions on a certain folder and its subfolders. I've configured the permissions on the parent folder to propagate down to all subfolders and files, as Figure 1 shows. As you can see, users have only Read and Execute access to the parent folder, but when I view the permissions of a subfolder that's a couple levels down, users have Modify access, as Figure 2 shows. What's going on?

Evidently, an intervening folder has the Inherit from parent the permission entries that apply to child objects. Include these with entries explicitly defined here. option cleared, which blocks permissions from folders higher in the hierarchy from propagating to this folder or its subfolders and files. To re-enable permissions inheritance, select the Inherit from parent... option for the subfolder.

If you're ever concerned that a folder's subfolders or files have blocked propagation, you can select the Replace permission entries on all child objects with entries shown here that apply to child objects option on the parent folder. When you click OK or Apply, this option will in effect bulldoze any explicitly defined permissions on child objects and re-enable the Inherit from parent... option on the child objects.