Their statement is a generic "you can't use our logo because of this law" (exactly what you'd expect from a government agency.) And their denied any involvement in this particular case (ditto.)

It is not protected under that law. Satire is most certainly allowed (and not just under First Amendment rights). The FBI tried to remove its seal from Wikipedia[0] and similarly miscited the appropriate law.

Sec. 15. (a) No person may, except with the written permission of the Director of the National Security Agency, knowingly use the words 'National Security Agency', the initials 'NSA', the seal of the National Security Agency, or any colorable imitation of such words, initials, or seal in connection with any merchandise, impersonation, solicitation, or commercial activity in a manner reasonably calculated to convey the impression that such use is approved, endorsed, or authorized by the National Security Agency.

It is that last bit that matters here.

[0] http://news.cnet.com/8301-1023_3-20012575-93.html

Sure, that's an arguable defense, but it's not like they're wrong in what they said.

You have to go to court to say, "fair use!"

I want to point out that "fair use" or, even more generally, First Amendment rights, are not involved here.

The statement that the NSA issued, that no one is allowed to use the Seal without written consent, is strictly false.

Section 15.a states explicitly that you may not use the Seal "in a manner reasonably calculated to convey the impression that such use is approved, endorsed, or authorized by the National Security Agency."

This t-shirt does not give you the impression that such use is approved, endorsed, or authorized by the National Security Agency. Fair use, parody, satire, doesn't matter.

I linked the CNET article because the FBI did the same thing a few years back:

"While we appreciate your desire to revise the statute to reflect your expansive vision of it, the fact is that we must work with the actual language of the statute, not the aspirational version of Section 701 that you forwarded to us," Mike Godwin, general counsel for Wikimedia Foundation, the nonprofit company that runs Wikipedia, wrote the FBI in response.

They omitted a large part of the law in their statement. You can't say "Endorsed by the NSA" on your product. You can say "The NSA Sucks." The use of the logo is allowed in the latter.