Why was the control group incorrect?
First, let me say this was a example that I studied in college in statistics to show the reason why you need to set up a proper control.
The gist of it is that in the 60s vaccines were still relatively new and not fully accepted by the population. Those who were fine with vaccines, and giving them to their children, at the time happened to better educated, and better educated people tend to be cleanlier. If you have a clean childhood, your immune system does not develop as much as those whom have an unwashed childhood (cant think of a good way to put that, but you know what I mean). So, the students who's parent did not give permission had a better developed immune, more likely to naturally fight off Polio (but certainly not 100%), and giving the vaccine to the child of the better educated group was just evening the playing field.
Therefore, there was no real difference between the groups.