I have a Windows folder mounted in Linux under a generic user account. This Windows folder has many subdirectories. In one of these subdirectories, "private", I set the permission so that only one user should be able to access that one subdirectory while everyone else can access the entire Windows folder, except the "private" folder. In Windows, the permissions work fine.

When I mount this folder in Linux, SAMBA is able to access ALL the files and subdirectories, including the "private" folder, which is supposed to be only accessible to that one user. Is this because of problems with NTFS and inheriting permissions versus Linux's FAT file system? I basically still want all permissions to apply when I mount this Windows folder in Linux. Yes, I have checked permissions and this generic user account should not have access to this "private" folder

Hope this makes sense

check the group permissions too.

you can make sure all the permitions are set right using crown and chmod:
crown 'user' 'privte dir'
chmod 700 'private dir'

and see if that fixes your prob.