Not to argue from authority, but I do have a degree in physics, so at least you know I'm not talking 100% out of my ass.
The thing to realize is that the exhaust gas doesn't stop the moment it reaches the chute, but recoils from it. That's also the reason blowing a fan into a sail actually does work, only rather poorly.
I'd also ask you to consider a thrust reverser and ask yourself what the difference is (conceptually there are none).
Imagine this scenario: You're standing on a wagon, holding a ball. You throw the ball forwards, off the wagon, and momentum conservation in the system means you roll backwards.
Now, imagine there's a wall mounted on top of the wagon, in front of you. You throw the ball against the wall, the ball stops dead and drops to the floor of the wagon. You'll impart momentum on the ball, and the ball will put it back into the wagon, and you'll have no speed after the ball has stopped.
Ok, now the crux: You throw the ball against the wall, and it bounces off the wall and lands slightly behind the wall. Clearly, compared to the previous case, there will result a forward net translation.
It's obviously much less efficient as a mode of propulsion than just throwing the ball backwards to start with (analogous to mounting the jet engine backwards in our case), but it does work.