Hightimecfi gave a perfect explanation of the snatch issue aerodynamics.
I think it is also important to emphasize the power of the control force in a fully developed situation. In the elevator case, Rich Ranaudo of NASA measured around 175 pounds of pull force in the Twin Otter during the one test in which they inadvertently let the situation get a little out of hand. That is more than he weighs, which says something about one's motivation in such circumstances.
Gilbert Defer of ATR discussed the aileron behavior during the ATR tanker testing following Roselawn. In this test, the ailerons rapidly oscillated back and forth...so it may not always be a straight forward snatch.
More importantly, with regard to the elevator case, is the change in stability, and then stick force gradient, prior to the snatch. As the stabilizer flow changes due to ice accretion, a nose down elevator input will lead to more flow separation and thus a marked reduction in nose up lift provided by the tail. The nose up elevator input "recambers" the tail and re-attaches flow, returning the tail to a full lifting capability.
So what typically happens in these events is that a slight nose-down input is called for, for example if one is a bit high on the glide slope. The nose-down input results in a radically larger nose down translation. The pilot responds with a larger pull force, generating a nose up input. The tail is re-cambered, flow re-attaches and the fellow gets the correct response to his mighty pull...a large nose up translation. Naturally, he walks right into the trap. He then applies a larger than normal nose down input, drastically de-cambers the tail, and gets a more substantial flow separation. The nose plunges, and now the required pull force can be enormous.
Keep in mind that throughout this event, the elevators still work; they change the lift produced by the tail.
In extreme cases, the stick force gradient may reverse. When this happens, increasing push results in less aerodynamic resistance, rather than more resistance as normal. Thus, a stronger push leads to far larger changes in elevator position than the same push does in a normally balanced situation. Now we have a really bad situation with the elevator moving far into the de-cambered profile.
Many of these type of accidents will have a small pitch down, followed by a strong pitch up, followed by a pitch down to the lawn dart position into the ground. Note that this is best experienced at speeds far above the main wing stall, so the two really don't co-habitate. One question which remains, and which I personally believe was significant in the Columbus J41 accident, is whether one can mistake a stick pusher for an elevator snatch. Based on my experience with the Fairchild Metro, I believe you could make this error if you were overly vigilant towards a tail stall.
The DC-9/MD80 series is capable of this, and it has happened. The difference is that full flaps are usually selected around the outer marker (or equivalent), allowing a lot of altitude for recovery. Turboprops, such as the Viscount and Jetstream, call for landing flaps much closer in. No altitude leads to no recovery. Even then, a successful recovery was achieved in a couple of the Viscount accidents initially...followed by an unrecoverable nose-over farther down the runway as the fellow tried to manage the stick force gradient problem. As we now know, retracting the flaps just one notch solves the problem.
I had the opportunity to fly the Twin Otter at NASA with Rich Ranaudo while ice shapes were on the tail. I have to say that you don't really appreciate things like longitudinal stability and stick force gradient until you try flying with them in a very altered state. You really have to understand how this beast will manifest itself in order to resist walking right into the trap.