What tends to do damage to soft flexible objects is pressure pushing outwards.
The human body is pretty complex, so lets start with something simpler, an inflated and tied off balloon.
Lets say we put our balloon in a pressure chamber. As we crank up the pressure the balloon will deflate such that the pressure inside the balloon remains slightly above the pressure outside it. The balloon will not be damaged.
Now lets say we put our balloon in a vacuum chamber. This time the balloon will expand to maintain the pressure inside slightly above the pressure outside. Eventually it will expand to the point of bursting.
Now lets say we fill the balloon with water instead of air. In this case it will survive in both the pressure chamber and the vaccum chamber, chamber
Now lets say instead of one balloon we have two, one inside a pressure chamber one outside it and the balloon are connected by a pipe running through the chamber wall. As we increase the pressure in the chamber the balloon inside the chamber will shrink and the out outside will expand and explode. This will apply regardless of whether the balloon are full of air, water or some mixture of both.
We can think of our body as being like a series of balloons, most of them are full of water but some of them (the lungs) are full of air and can be opened to the air.
IF someone dives without breathing apparatus then the lungs will compress but this doesn't damage them. If someone dives with breathing apparatus then the breathing apparatus will keep the pressure in their lungs at roughly the same pressure as the water pressure while allowing the lungs to retain their normal size. If someone descends using breathing apparatus and tries to hold their breath on the ascent then damage is likely.
In the mythbusters experiment the fluids in the body are pushed from the body of the suit to the helmet, bursting anything that tries to stand in their way.