Weird NTFS Permissions Issue - VERY Strange

[GLT]

We've since migrated to Server 2003, but we need to keep an NT 4.0 BDC online
for awhile, so we are in Mixed-Mode. Problem is, strange things are happening
when you attempt to set NTFS Permissions on this NT 4.0 BDC (Service Pack 6a).

Off of the Root of C:\ are two folders created a few moments apart as a test
to address this same problem that was discovered today:

Created Folder-1
Created Folder-2

Root Share: Everyone Full Control

Folder SHARE: Everyone Full Control on both.

NTFS Permissions on both:

Folder-1 is set for Administrator, Domain Admins at the NTFS Level. No other
Users or Groups. No one else can get in. Access denied. End of story.

Folder-2 also is set for Administrator, Domain Admins at the NTFS Level. No
other Users or Groups.

Here is where it is strange: ANYONE can breech Folder-2 across the network,
despite it's IDENTICAL permissions.

Any idea what's going on here? Same Permssions, same disk.

Thanks!