Structural rating of aircraft to withstand storm induced structural stresses
All aircraft can in theory be overstressed by either a vertical gust (flying into an updraft) that is severe enough or a maneuvering input (pulling on the stick) that is hard enough.  Both increase angle of attack suddenly increasing the lift force, and bending, on the wings.  Increase the lift force enough to exceed the bending strength of the wing's spar, and that's all she wrote.

The protection from this comes from the fact that if you are below a certain speed, you will exceed the stalling AOA before the bending load exceeds the limit, and the stall will partially unload the wing before it gets over stressed.

So there are two speeds you have to observe; Maneuvering Speed and (on larger airplanes) Turbulent Air Penetration Speed (also called Rough Air Speed).   Maneuvering Speed is the speed below which you'll stall before over stressing the wings if you just yank the control column back as hard as you can to full travel.  Instead of pulling the wings off you'll just snap roll (which is in fact, with rudder added, how you do a snap roll).

Turbulent Air Penetration Speed is the speed below which an extreme vertical gust will take the wing past its stall AOA before the gust can exceed the wing's bending strength.

On transport airplanes, if you know you will, or expect there is a significant risk that you will, enter turbulence, you slow the airplane to Turbulent Air Penetration Speed as protection against over stress.  You would do this if there are thunderstorms in the area (you still give storm cells a wide berth in any case), or there are reports of Clear Air Turbulence, or you are crossing the boundary of a jet stream at altitude, where CAT is typically found and you are being cautious.

On the CRJ700, the Turbulent Air Penetration Speed is actually in the lower end of the normal cruise range, 280kt/.75 Mach, so it's not a major inconvenience.  Maneuvering speed is well below that.

Light aircraft like the Piper Saratoga in the video don't usually publish a Turbulent Air Penetration Speed, just a Maneuvering Speed (134kt for the Saratoga), and the pilot should have slowed to that to avoid being over stressed from turbulence.  

Problem is, light airplanes bumbling into thunderstorms usually end up in spiral dives where limiting the speed becomes impossible and they typically come out the bottom of the storm in pieces from over speed and/or over stress, and it comes down to staying out of them at all costs.