What is the effect of permissions on external drives?
Anyone with the same user ID as you have on your main machine will be able to read the disk. The, usually hidden, user Ids start at 501 and increase. If you are not the first user on a machine you will not be able to read the contents of the drive.

I've gone round and round with this. If you need a secure drive then you need to encrypt it with a password. There are ways to do this using the tools built into Mountain Lion, or you can use a third party solution like True Crypt.