If the plane was not offloaded, nobody was technically on Kazakh soil... I would assume that is how it works.
Now, if the crew had said, "No, cannot, will stay here"... How do you think they would have managed pax without visas?... And this poor family?... Quite possibly the Kazakh's may have said "cannot... Refuel and depart...". So, min rest on board, and a deceased baby, who may not be in great shape after 12 hours.... Seriously, just think about that.
So options... Russia, China, Mongolia, India ?? None of the above are particularly appealing. Possibly no better as a stop, and India??? The beauracracy there is nightmarish on a normal day.
So, discretion.... If there was an agreement from the crew to utilize Commanders Discretion, and if they decided that they were up for it, why not? What is the difference between using 1 minute or the full extent of it?
I bet you have done it before, and probably for lesser circumstances than those facing this crew.
Stop giving this crew a hard time. The only thing difficult is the fact that the company is the one who expects us to fly over inhospitable countries, and terrain, and now with one less crew member and a heck of a lot less options - reducing safety drastically - for the cost of a single second officer, who would be a dollar per passenger ticket, if that.