Allowing Apache in Ubuntu to access files in NTFS hard drive

What you are looking at is known as Special Permissions. I would highly recommend you read this article at Windows Security that covers and explains in detail how security on NTFS works.

Warning: Be careful when testing security with IIS. IIS has another layer of security which is not linked to NTFS, however it will enforce NTFS permission. Also locking down folders for a specific user will not affect anonymous website access, where IIS uses it's own account, and not the logged in user, to specify access.

Depending on how the files were added and how badly the folder is fragmented the quickest way might even be to move off the files you want to keep and nuke the partition!