These kinds of statistics are pretty interesting, but it's not the full picture either. The number of participants per country is limited.
China cannot send one billion people to the Games. Otherwise we would probably see more Chinese divers or gymnasts who could snatch gold. USA can send only team in Basketball, even though USA II might have chances to win gold as well. And so on.
Also, one outstanding athlete from a small country, say Marc Girardelli for Luxembourg in skiing, can have some big influence in the adjusted medal table, while the same outstanding athlete for USA doesn't.
Sure, the big countries still have better opportunities than San Marino or Micronesia. But it's not as easy as a 1:1 comparison between their number of medals their population.