The saying at the end refers to how surnames overlap a lot in Japan – Satō and Saitō being the most common. In English, I guess an equivalent would be Smith and Jones? I think it's because in Japan, if you're married, you're legally required to have the same surname.
To better visualize the problem for Japan, imagine you're at the front of the classroom. Look at a couple of columns of maybe a dozen students at their seats – that there are all Watanabe, and not a single one of them is related to another.
