The difference is of course that you do get information in the Monty Hall setup, and here you get none, if I read that correctly.
In fact, the fake/paradoxical solution probably plays on the reader's familiarity with the Monty Hall problem. ("Ah yeah I remember this. Switching is better!")
Exactly what I thought too. I find human behavior in such situations fascination. Have penned some thoughts on it - have a read if you like