The courts seem to disagree with you on this point as it pertains to national security letters.

I haven't read any of the legal decisions; they're long, and I'm not a lawyer, but I see a big hole in the argument you're making. In every non-pathological case I can think of, a person receiving confidential information that they'll be prohibited from disclosing agrees to the confidentiality first. You can't send me an unsolicited letter containing information you want kept confidential and sue or jail me if I disclose that information, but the FBI can (pending the outcome of their appeal of the ruling that says they can't).

The first amendment guarantees free speech from being prosecuted criminally, not civilly. If your speech causes harm to come to someone or someone's property, then you can be prosecuted criminally just the same as you can be prosecuted criminally for using a rock to bring harm to someone. You have the right to throw rocks, but if you cause harm to come to someone then you can be held criminally (and civilly) responsible.

This is not a situation where someone's speech can be said definitely to cause harm to someone. Therefore the first amendment guarantees you will not be criminally prosecuted for it, though the government does not care.

Disclosing confidential information is not protected by the first amendment because it is a civil matter, not a criminal one. The federal government could (within the bounds of the constitution) bring a civil case against someone who violates the gag order, but it would be an uphill battle for them because the person violating the order did not sign a contract agreeing to keep quiet.