It is not at all clear to me that a decaying orbit, because atmospheric drag, is somehow a refutation of Newton's Law of gravity. Or that the math in the orbital mechanics, based on these theories had something to do with this particular decaying orbit Not to mention the fact that while this satellite achieved the correct orbit (theories), it malfunctioned so normal orbit corrections to keep the orbit stable (because of atmospheric drag) didn't really happen.
As every school child knows, an orbit is a line of trajectory around a mass body, but not necessarily one that is stable, circular or even making a circumnavigation around the body, and it takes at least two firings of rockets, or path adjustments or combination thereof (human technology) to place a body in an orbit around around a body. It has to do with physics.
This is from wiki:
"The main proven technique involves launching nearly vertically for a few kilometers while performing a gravity turn, and then progressively flattening the trajectory out at an altitude of 170+ km and accelerating on a horizontal trajectory (with the rocket angled upwards to fight gravity and maintain altitude) for a 5-8 minute burn until orbital velocity is achieved. Currently, 2-4 stages are needed to achieve the required delta-v."
Essentially, an orbit that is too circular, and too close will start to lose energy from atmospheric drag, and to some extent, depending on the satellite's configuration, electromagnetic drag (metal parts can start building up current by flying through the EM field, and this gets converted into heat, which slowly builds and slowly dissipates in the near vacuum.), which tend to make the orbit more circular, hence losing energy, so the satellite essentially spirals into the gravity well, as did 193.
The atmosphere expands and contracts mostly because of solar activity. The expansion can cause satellites higher than 200 km to experience higher drag. That is why the Space Station has to get boosts into higher orbits, along with other satellites, like the Hubble. For 193 to have stayed in a more stable orbit, its perigee probably needed to be 10-15 km higher, which the DoD could have adjusted and compensated for, if they hadn't lost communication with 193.
The theory holds just fine, it was the engineering that botched it. I think the fact that they could hit this 17,000 mph satellite with a missile fired from a boat bouncing around on an ocean on a planet spinning at nearly 1,000 mph suggests that the theory and the math derived from the theory hold.
yo, orbital mechanics, family fun!