Exactly: what counterintuitively changes the overall probability of picking the correct door is Monty’s introduction of new information that biases the contestant to the right choice. Many years ago I was in such disbelief about this result that I wrote a little Monte Carlo simulation to “prove” I was right. In fact, it proved I was wrong!
The original problem formulation lacked it. Also this comic lacked it. Most people who describe the problem doesn't include the titbit. It is a very misunderstood point, you can even see it everywhere in this thread.
You're entirely right, and in your other comment as well. I just recognized this was about Monty Hall and didn't even bother reading the details. I also assumed other people would do the same: mentally invoke the entire paradox. It is indeed true that someone discovering the paradox with this comic wouldn't have nearly enough info to understand it, and would be correct to say it's wrong.
Based on him knowing where the prize is, it’s hard to escape the idea that he’s only showing you a new door because you picked the right one, therefore intuitively you feel like you should stick with your guns. At least if you’re wrong the way you chose, you won’t feel like you’ve been manipulated.