What is junes reaction to days theory about the republic giving its own citizens the plague?

Day's theory was that the Plague was spread by the Republic, not by natural causes. This theory is also shared by her brother, Metias, who created a secret blog for her before he died, telling her what he suspected. The more June mulls it over, the more she comes to accept it. She eventually strikes a deal with the Patriots for their help, freeing Day on the morning of his execution. However, his brother John dies in his place.