Rather than coming to a conclusion, he seems to be starting off making a point, then using all those calculations to "prove" it.
Essentially he seems to be saying that people, particularly those with no linguistic training, tend to see cognates and patterns in sounds and meaning(s) between languages, when statistically they are likely to be due to chance.

I can't argue either way, certainly. There are the physical limitations of the human speech structures--which is more of an argument for coincidence. But it seems to me that his parameters are rather arbitrary--though frankly I don't know how else he could have established them! But I can't help thinking that his numbers would be more accurate if: a.) we knew how things were pronounced in ancient times; b.) they took into account b.1.) travel and b.2.) regional accents and dialects.

Yes, I know that if he/we had that information, this whole question would be moot. But my point is that, no matter how intricately he delved into the numbers of known "phonetic leeway", I think there are too many unknowns for these numbers to be considered accurate.

It just seems to be one of those unanswerable questions; in any example, is the similarity pure coincidence or is there a piece of history that we're not aware of?