You could make shoutaddpal.php check the poster's status and if they aren't an admin then just return them back to the shoutbox without adding the post. Shouldn't be to hard.
Being logged in as an admin you should be able to delete any shout in the shout box though by clicking on the box with the x in it. I don't know why you had to actually go in from that side of things to delete the shout. Are your cookies site wide?
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