According to this post, Team Build’s <UpdateBuildNumberDropLocation Task has code in it which needs to update permissions on the drop location. From what I understand, the code will change the permissions so the App Tier service account has access to the drop location (it needs access to delete builds and such). To see this, Right Click on a file located on the drop location and notice how the App Tier service account has full access to the folder and any sub files or directories. The <UpdateBuildNumberDropLocation is doing this.
The issue that I’m running into is, when the drop location is a NFS system, there are no permissions at the file or directory level. So the build fails because permission can't be set. But when the drop location is a NFS mount, there are no file/directory permissions.