Not only is there going to be variation from one phone to another, there’ll be variation from place to place on the same phone. If someone does go out a measure a few white iPhones and finds them to be several (not just a few) thousandths of an inch thicker than black iPhones, I’ll be convinced there’s a difference.
He also shows that his black iPhone 4 is thicker than his son’s black iPhone 4 and how one should photograph these things. But this makes the most sense:
Wait. Before I do that, let me digress and say that the best way to prove a difference in thickness is to measure the goddamn thicknesses. But perhaps this is too technical a solution for a “marketing guy.”