" I wanted to make the backup partition read-write for root and read-only for the users."
I have a backup set up the way that you want and have never had any trouble with it.
You can try changing the permissions of the mounpoint directory to 755. Unmount the partition, change the permissions of the mountpoint to 755, and mount the partition again.
Here is my /etc/fstab entry for my backup partition:
/dev/hde3 /backup ext2 defaults 1 2
Be prepared. Create a LifeBoat CD.