Pentagon, yes. But NASA isn’t really allowed to run secret programs. They just keep secrets on the public programs they do run, such as what certain satellites are for when the shuttle deployed them.
Surely NASA has the ability to fashion nooks and crannies that escape routine public disclosure requirements. For example, NASA might do a joint project with the DARPA, with the project governed by military secrecy until NASA and DARPA agree to issue a public report.
They just keep secrets on the public programs they do run
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Such as Apollo where many Hasselblad photos in their catalogues are missing, wrongly cataloged, blurred, altered via razor blade (P’shop of the day), and otherwise changed. NASA is a ostensibly a public program that falls under DoD over-site. All back-channel Apollo communications are still classified or otherwise not available to the public. Even many images taken by the Cassini Probe have disappeared from their website. As well as many images taken during the early days of the ISS and Shuttle missions. Early Mars mission images have suffered the same fate.
NASA has lots of secrets. We’re just not supposed to notice, and when someone does they are publicly ridiculed etc.