Hey Com jam.Its very simple. Any unidentified bogey outside of the 200 radius from a CVN is just a possible threat.Once it cross's inside the 200 mile circle it then become's a target unless identified as a friendly! This is something the Captain of the ship takes very seriously as he only get's one chance to get it right when something is closing on his ship at 400 kts!
Based on your reasoning Iran's forces would have the same right to shoot at anything within 200 miles of their borders that is not identified as friendly!
And how does climbing exactly qualify as "closing on his ship"?