international Law, NATO, and common sense
No long discourse on the several principles of international law called into play by the intercept and shoot-down, but a few points should be noted and kept in mind. The first of these is that the use of force most generally depends upon whether an "armed attack" has taken place. A quarter-of-a-minute incursion into a State's sovereign airspace, by itself and in and of itself, most probably does not fall within the widely accepted definition of the concept of an "armed attack." Second, even where the use of force is approved (or at the least, not disapproved) by applicable international law, such action generally is required to be both proportionate, and taken only where necessary. Each person may draw their own conclusions as to the question of necessity here, and similarly as to proportionality (though the reasons or factors relevant to those two standards may be different; "prior warnings" count for something, but how much?). Third, the fact - if (and I do mean, "if") it is one - that Turkmen were on "the receiving end" of Russian air-to-ground weaponry certainly makes the point better than any pedant could: where military commanders see vital or significant national interest at stake, what international law says about their range of actions may be, well, pedantic.
Thus it was unsurprising - from a legal standpoint - that NATO fairly rapidly issued a wish list often summarized, after the fact, as "cooler heads prevailed."