You're welcome. No, you do not need to remove the cowling to stop a boat at any time, for any reason.
IMO/IME unless there were problems with the motor, there is no reason at all to remove the cowling while out on the water. The most common reasons to remove the cowling would be for maintenance (oil change, lubrication, winterizing, etc.) or to make repairs. Both maintenance and repairs are typically done either in a dock slip or by putting the boat on a trailer and pulling it out of the water to work on it on dry land.
I've been legally piloting boats for 45 years and have never once had a need to remove the cowling while out on the water. Now, if their motor broke down while out on the lake and (1) they didn't have tow insurance
and (2) there were no other boaters within sight to offer a tow, I can see a mechanically inclined boater removing the cowling to try to make repairs. IME, boaters are a fairly generous community. I cannot tell you how many times I've towed a total stranger's boat back to their dock or a marina.
Another thing to note is that boat motors have a kill switch. These are a switch on the motor you attach one end of a lanyard to and then attach the other end of the lanyard to the person piloting the boat. If the pilot gets too far from the motor or is thrown out, the lanyard is pulled out of the kill switch and the motor shuts down. In fact, you cannot start the motor without the kill switch in the Run position (see first picture). However, speaking from experience, it's very possible to connect the lanyard ONLY to the kill switch
OR to not insert the lanyard at all and simply use your finger to flip the kill switch to the Run position.
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Note in the above picture how one end of the lanyard is connected to the stern of the boat and not the pilot, since the kill switch is in the run position, the motor would start.
This is also perplexing. As stated above, IME/IMO the only reason for them to have removed the cowling is if they were having problems with the motor. The only explanation I can thing of is *maybe* JW was taking pictures of GJ working on the motor for social media or something like that.