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.
Yes, plenty of secrets but no big secret programs.