Brazilian authorities claim that U.S. swimmer Ryan Lochte made false claims about being robbed. However, Brazil is has faced widespread corruption throughout its government. Therefore, the Brazilian government may very well be covering up the robbery to protect the country's image. It seems odd that an Olympic athlete would make up a story about being robbed. The likelihood is that the Brazilian government is making up the story that he was not robbed.
The robbery incident with Ryan Lochte and others will require a full investigation so there may be more details that are uncovered. It would be very unlikely that several U.S. swimmer would create this robbery story. They are not in need of the media attention or looking for any conflict in Brazil. The authorities may be trying to cover up any scandal to protect themselves.
Not sure the reasoning behind detaining these men in Brazil, but there is definitely more to this story that what is being told. People are mugged or robbed daily around the world. This in and of itself is not news and I am sure that during the Olympics, more people than the 4 swimmers in the incident have reported being victims of criminal acts. I don't know what's going on, but there is definitely more to this story.
By seizing Ryan Lochte's passport, the Brazilian authorities are drawing more attention to the case than it would otherwise have received. They must have genuine concerns about the U.S. swimmer's claims, otherwise they would surely just let him travel back home while they continued searching for the criminals. The Games are nearly over so it is not as though they are worried about putting people off coming to the country.