Should the controller have concluded there was a pressurization problem from that transmission?
No. What the controller should have concluded was there was a problem with the airplane.
Now, once the controller concluded THAT, he should have done something other than exhibit indifference to an undeclared emergency. ATC didn't know EXACTLY what the "problem" was, but they DID KNOW that there WAS a "problem."
IMO, if a pilot calls ATC and says "I have a problem with my airplane and I need to descend" that sort of says that MAYBE that airplane could fall out of the sky (which it did in this case eventually). That "MAYBE" should have been enough for the controller to move the OTHER aircraft out of the way and give priority to the problem aircraft.
Add to this is the idea that if I were in another airplane and someone heading at me said "Ummm, there's a problem with the airplane here.." I'd WANT the controller to divert
me instead of telling the plane with the flying problem HE's the one who has to turn and wait a bit until they can find time to get back to him on his problem. Having a flaming ball of wreckage hurtling at me from 28,000 feet would ruin my day.
As for the idea that pilot not saying the "magic words" means there wasn't an emergency; exactly what do you think happened when the pilot stopped saying anything? That's right, they scrambled jets because there was an emergency. Which word apprently no one actually said. So, requiring the "magic words" to be spoken or there isn't an emergency ignores reality.
Now, having said all of that, the controller probably isn't
legally liable. However, he is culpable for contributing to the death of 2 souls through indifference or neglect. The FAA is also maybe equally culpable for failing to properly train controllers to recognize potential emergencies and deal with them in a manner which treats the potential emergency as a priority rather than "We'll get back to you on that..."
PIC, busy, tired, AIM, FAR, should have, would have, yada yada yada are all just excuses. The plane had a problem and problems get fixed ON THE GROUND, not at 28, 25, 20 thousand feet up.
But hey, what do I know. I'm just a low time fomer student thinking about restarting my training...