Of course it does follow. If you look at how the FEC regulates campaigns, they do so by creating intricate and/or vague rules, which they can subsequently enforce against any speakers or type of speech within their purview. When any government agency is allowed to regulate something, they are given a great deal of deference by the courts and the legislature, this administrative discretion "necessarily allow[s] the FEC to selectively silence any group or type of speech they dislike".
Of course it does follow. If you look at how the FEC regulates campaigns, they do so by creating intricate and/or vague rules, which they can subsequently enforce against any speakers or type of speech within their purview. When any government agency is allowed to regulate something, they are given a great deal of deference by the courts and the legislature, this administrative discretion "necessarily allow[s] the FEC to selectively silence any group or type of speech they dislike".