Are you saying we shouldn't expect a military satellite to have some semblance of simple authentication?
It sounds like what they built was literally a simple repeater. If that's the case, they shouldn't have a problem with this "unauthorized use," because by design, there is no such thing.
(The preceding assumes the pirate is licensed to transmit in the 1.25m band that the article noted as the uplink.)
The uplink freqs are not any that are licensed for any amateur use, these flights are operating between 250-350 MHz.
Edit: look what I found http://mt-milcom.blogspot.com/p/alphabravocharlie-frequency-...
Bent pipes are perfect. Not everything needs to be overengineered to hell. A handful of pirates aren't a big enough deal to boil the ocean with a DSP. And assuming that the signal is Manchester-coded, you can defeat the pirates in future models with a simple analog filter to remove their noise.
It sounds like back in the day what I described above wasn't an issue.