Correct. In missions like STONEHENGE RETURNS I, all messages are sent to everyone. However, in non-Special Raid missions, you have to hold down the right D-pad button instead of a simple press to send to everyone.
Yeah, it took me a while to figure out how to do it, but when you are in a mission, press the "Start" button on the controller, and it will show you how to do it to all members. Just like what the others said, you have to select a message, and hold the right D-Pad button down until it goes over to other teams.