The reason chimpanzees can exert more force is anchoring, their muscles are anchored to the bone further form the joint so they have better mechanical advantage. A human has a much wider range of movement, though, and I believe we better maintain force under movement. So which a chimp might be able to lift themselves more easily, a human ends up being able to throw a rock or spear much further.
EDIT: Also, ekianjo is right that lifting cars is an exaggeration.
The flip side of having crappier levers for force, is that we have better levers for precision.
Lifting cars is often an exaggeration in terms of wording, the reality is usually lifting up one side of the car, which is very different in terms of weight.
I'm pretty sure the safeguard here is the Golgi tendon organ
http://en.wikipedia.org/wiki/Golgi_tendon_organ
http://en.wikipedia.org/wiki/Golgi_tendon_reflex
The Golgi tendon reflex operates as a protective feedback mechanism to control the tension of an active muscle by causing relaxation before the tendon tension becomes high enough to cause damage.