You're falling for the media spin (and perhaps I contributed to this in the context of this discussion re: HANSON) that this is a matter for the criminal justice system, ergo the emphasis on Fourth Amendment violations. This is a war fighting issue, plain and simple, involving military secrets and the collection of military intelligence, the fact notwithstanding that al-qaeda wears no uniforms. Had the third reich the ability to transmit instructions directly to their operatives in the continental US, do you think Eisenhower would have had his intel folks seek a warrant? The NSA is primarily a military agency staffed by military personnel, and was used in this capacity for the gathering of military intelligence.
Having said that, the classification authority in the military is the generating office, and the various classifications (FOUO/Confidential/Secret/Top Secret) are assigned based on the potential impact the unauthorized release of that information would have on the US's national security posture. While I don't have a lot of details regarding what had been leaked to the NY Slimes, I'd be comfortable, based on what I have read, in betting a considerable sum of money that they had been provided access to at least Secret level material, and most likely higher.
Well, no. The only place I've even seen this fine distinction in terms of the NY Times is right here on FreeRepublic.
See, e.g., Pentagon Papers which were classified.