As a Canadian, living in Canada, a country with NO "fair use" provisions because our laws are derived from those of the United Kingdom, I am well aware of how copyright and trademarks work. The Olympics are a rarefied, global, multinational corporation that demand governments bend to their will with respect to their trademarks if they want the games. Governments do so because it brings in revenue and also allows them to undertake mega projects that would otherwise never see the light of day.
Also: For the 2010 FIFA World Cup the airline Kulula called itself the "Unofficial National Carrier of the You-Know-What". The ad was pulled when a complaint was lodged, though.
For a website with so many startups you think people would be a little more aware of how copyright and trademarks work.