The webpage you linked seems to show a circuit running on a battery.
In this case, the chassis just acts as a wire completing the loop back to the negative terminal of the battery. You have no danger of being shocked because the current MUST travel back to the battery.... It will not go to ground through you. Think about the 12 V battery in your car... you can tap off the positive RED of your car battery and then basically complete the circuit by touching any other part of your car metal chassis.... because it is connected to the BLACK negative terminal. The metal chassis just completes the circuit to the negative terminal because it is connected to the negative terminal.
There is no danger of current jumping into you and into the ground... just like there is no danger if you touch only 1 pole of a battery.
Now on the other hand, if they are plugging the chassis to the MAINS.... that is a different story. It must be the green ground wire that connects to the chassis to avoid it getting charged with respect to ground (and you which is also "grounded" essentially). The chassis is essentially equipotential to the ground. If you are NOT grounded... like when you are wearing rubber shoes and you rub your head on a blanket and get charged up with a lot of static.... you WILL ground yourself and experience a painful shock and see a spark if you touch something that is grounded (like a metal pipe, a grounded chassis, or whatever).
There is no way the chassis is connected to the active "live" wire or you will ground it when you touch the chassis (unless you are wearing rubber shoes) and you will get a shock... just like when you touch the white wire from the AC mains by sticking a screw-driver into the plug.
If the chassis is connected to the neutral wire, that is a different story. However that is not a good practice especially if there is a non-polarized outlet or plug, you could slip it in the wrong way and swap the neutral and active. Also, the neutral is not grounded all the time... it floats a bit with respect to ground, and you could get a bit of a zap even touching a neutral wire, so you should avoid it. But it is certainly better than touching active.