The government's special responsibility has two bases. One is that you can't sue the government for false and defamatory speech. If I accused Obama of wiretapping my phone, he could sue me for libel. If my statement was knowingly false, I'd have to pay up. On the other hand, if the president makes the same statement, he can't be sued in his official capacity. And a private libel suit mostly likely wouldn't go anywhere against a sitting president — for good reason, because the president shouldn't be encumbered by lawsuits while in office.