How can an airplane be allowed to carry passengers when the margin to airframe disintegration is so narrow?
There are certification bodies in the US, Europe and many other countries that define what that margin is. The greater the margin the heavier the plane will be, the more fuel it will need and the less load it will be able to carry. So your question really is asking if all these certification bodies are idiots. They are not and are definitely better at it than your armchair speculation. Simple evidence is looking at the rate of crashes and fatalities over time despite the increasing amount of air travel.
How come you don't walk around always wearing a bulletproof vest? Why aren't all your house doors, windows and walls armoured? Because there are costs and benefits and they all have to weighted together to come up with something appropriate.
but to be able to tear the airplane apart in level flight?
It would not tear apart in simple level flight within the normal speed range. It could be torn apart going too fast (ie beyond the certification limits imposed by those national bodies) but even then would not be in level flight but likely dropping. It was a massive thunderstorm with huge air currents they were going through. This is an example of what planes can survive where the plane looped, parts flew off and the wings got permanently bent. This is an example of a certification test for wing strength. FAA regulations require that wings survive 1.5 times (150 percent) of the highest aerodynamic load that the jet could ever be expected to encounter during flight for 3 seconds. That applies to all airliners. The pitot tubes keep being mentioned because they tell you how fast you are going relative to the surrounding air. If they iced over then you don't know and going to slow will result in a stall, going fast increases discomfort and going too fast can result in bits of the plane breaking off.
But to be clear it required abnormal circumstances to break apart. Way beyond anything normally or abnormally encountered. If the circumstances happened with any regularity then you would hear about this kind of accident more often.
If the airplane can send fault messages home, why don't blackbox data streams get sent as well? At least that way there would be some situation info available as opposed to none.
The fault messages are generally intended for maintenance so that when the plane arrives they can be repaired as quickly as possible and the plane turned around. They also help with long term tracking of wear and tear. Current blackbox recorders record a huge amount of data which would be infeasible to transmit, especially when it has to go via satellite such as when over oceans. Plane crashes are very rare (that is why they make the news) and it is even rarer to not find the blackboxes.
In some ways reliance on flight computers is like reliance on spreadsheets or calculators -- if you do not understand what is going on and are not capable of doing it yourself then you cannot tell if the software is correct. Essentially, if the computer says it is so then it is, and you either survive or not.
You overestimate the ability of humans. We are long gone from the days of the lonesome hero sweating it with the control stick. A flying plane is a complex mechanism. You have many control surfaces, air pressures and speeds, centre of gravity, fuel consumption, engine abilities, aerodynamics etc all to take into account. A computer program can do all of that so many times better than a human which includes being both more economical and reacting quicker. The people who make planes are not idiots. Ultimately you have to take the underlying tools you use as is. For example I don't see you insisting on design your own CPU - you just use whatever is in your computer. The airplane manufacturers have user (pilot) interaction teams to try and provide the best interfaces possible. For example the Airbus team decided that the computer could feasibly compute safe flight angles but humans are unlikely to, so a human can pull the stick bar as far as the want but the plane will only obey it as much as is safe. Boeing provide force feedback on their control sticks in the 777 but that information is synthesized (ie fake). They also have modes where the computer hands over more control to the pilot such as when the computer is unsure of the readings it is getting or the calculations do not make sense. (I believe pilots can also manually select these more control to them modes.)
But if you think humans are so much better look at how many managed to kill themselves in the earlier days of aviation, or at the way people "pilot" cars today.
If you genuinely care about this sort of stuff then I'd recommend studying and working for the regulators or design companies and seeing what difference you can make.