At the risk of giving away a poorly guarded secret:
He does this as a way of pinging you to determine whether you are currently in a battle or not. If you aren't he gets the "Invitation Sent" dialogue, if you are he gets the "Player not in chat" dialogue. He is trying to time his battles so that he either gets matched up against you or can avoid you.
I'm sure the ability to use the invitation function this way was unintended and it would be nice to see that ability removed. Perhaps you get the "Invitation Sent" so long as someone is online and if they are in a battle you just sit there and wait until you cancel the invite.
Turning off all battle invites removes the annoying barrage of invites from your screen but allows him to continue using this tactic without you even knowing it.
+1 to you!!
That's a brilliant technique, however sneaky and annoying it may be