Your story sounds an awful lot like the plot for the movie "My Cousin Vinnie".
Police pull over the wrong people all the time. People who are innocent do get accused of crimes.
Our Bill of Rights protects us from the abuses of overzealous police officers and prosecutors. The downside is that it also protects the rights of those who do commit crimes... but I would rather have the system we have in the US than any other country in the world.