The way I parse it out is we have a general rule that DM decides when a check is called for. The hard constraints on DM are that it must be something possible, not certain, and with consequences for failure. Who judges? DM is instructed to "ask yourself".
We then have a couple of examples of what might be impossible. Hitting the moon with an arrow. Picking a lock without tools one is proficient with. It is abundantly clear that these are given (in legalese) without limitation: meaning they are not exhaustive.
The upshot to me is that each group decides what is possible at their table. Now, should they be consistent in such judgements? I believe the normal finding on that is "yes"... consistency is valued. That implies that as judgements are made, a local rubric is formed.
It is entirely reasonable if one group's rubric comes to include requiring proficiency for some undertakings. After all, one of the handful of examples does exactly that! And on the other hand, it's entirely reasonable if another group's rubric excludes it (beyond tools.)
Neither group can reasonably insist that the other is mistaken in broader cases. Again, the exemplification is meagre, and even were it not it would be necessarily incomplete. Who must the DM at each table consult? Themselves, per RAW.