Of course, what we're really saying here is that we can censor people we don't like. Free speech is conditional on you only saying things that no one minds you saying anyway...
Yes, it is actually. It sounds counter intuitive right? But all classified means if that the president (or someone under him) does NOT want something published. So if publishing something classified is not free speech then what is? You don't need the first ammendment to publish things the government does not mind you publishing, you already have their permission. The whole point of the first amendment is to protect publishing things the government doesn't want published.
If the government could actually prevent publishing of anything it classified, the US would still be fighting the Vietnam war and we would all consider Nixon to be a stand up guy who fairly won re-election...