Okay, I'm gonna try to take the mathematical approach here. When you combine two waves, they are summed ... if each wave has a peak with a value of 1 at a particular sample, the summed value of that sample is 2. Likewise, if one wave is +1 and one is -.5, the result is a .5 value at that sample, and so on.

At any given sample, each 16-bit sample can have one of 65536 discrete values. When you add them together, two summed waves can have one of 131072 values. By the math, Scott's theory holds. It takes an extra bit (now at 2^17 values) to hold two summed waves.