Bureaucrats aren't known for their out-of-the-box thinking. Probably half the staff at the NSA could figure out how to get the data off the tapes, but the person in charge of this isn't that cleaver and might think that there could be something classified on them. Either in plain sight or as in the form of some sort of Steganography. They can't leave the building with the tapes and they can't use someone else's player as it might be bugged. "The Thing" probably still spokes the hell out of them.