It is surprising that you would read an article by noted foreign policy expert Mr. Richard Haass to 'over read' relative foreign policy influence of various countries based on London Olympics medal count. I was hoping to read the paragraph about 'qualifying such over reading'; but I did not find any such guarded advice from Mr. Hass.
Take the case of Germany and Spain. By all accounts Spaniards and various Spanish Sports Teams have been on ascendance lately regardless of their Olympic medal count (which is not bad as well) whereas Germany is not able to produce any significant results in competitive international sports commensurate to it's former sporting power status. But fact is regardless of Germany'a medal count in London Olympics; Merkel's Germany exerts far more influence globally than what was the case at German unification time in early 1990s when Germany had probably her best Olympic performance. On the other hand despite Spain's great success in Sports, its economy is no good. One can even make an argument that despite weak Spanish economy, it is amazing that it continues to do so well in so many different sports - Soccer, Cycling, Basketball, Tennis and many others.
Another hole in Mr. Haass's argument - it is all right to laugh at India for her performance in Oympics; but you cannot forget that India is the current title holder of Cricket World Cup. Cricket continues to be popular in India and Indians are consummate fans of that game. Without understanding contribution of Indians in the world of Cricket, to solely judge India's relative worth on Olympic medal count is a very loop sided observation.
What do you say of Israel who failed to win any medal in London Olympics? Here is a tiny country which exerts such an enormous influence on the Global Cop (USA) that it's Presidential Candidate Romney - possibly next president - is completely in the pocket of Israel and who is ready to jump as high as warranted by Israeli PM Netanyahu. Israel and Republicans are ready to create the havoc of Iran war at earliest possible time. That same Iran is on weaker wicket despite sterling performance by its Athletes in London Olympics.
Same is the case with Pakistan too - the country came empty handed in London Olympics; but it continues to harass USA mighty and its trouble making potential is enormous.
Point is don't over read in result tally of Olympics. Those Olympic medal tallies are all good as bragging rights and marketing ploys only. Serious business of foreign policy is quite different.