Player: I want to do an impossible thing.
GM: ....roll a skill check
Player: HAH! Natural 20, the impossible thing happens
And when it is not a natural 20, or other form of critical success making the impossible happen it is the other way. The GM calls for a roll, someone fails, and so some horrible, inexplicable thing happens and the GM has to pause the game because now they need to figure out what is going on.
Now I get the idea behind these stories. With the first option the player is trying to follow the "Don't say no" rule. With the second option the GM is trying to stay true to the game which says if there is a significant chance for failure, there should be a roll. The only problem though is this simple rule: the dice are not your friend.
I mean, don't start looking at your dice bag suspiciously. The dice are also not your enemy. They are the physical form of random chance. And no matter how low the chances are of something happening the only thing you need to know about low probability events is this: sometimes, shit happens.
If you call for a dice roll in response to a player stating they are trying to do something, you are saying that the possibility of it happening exists. So if a dwarf goes overboard and the player says "I flap my arms like wings" and you tell them to roll athletics, in that moment you are giving legitimacy to the idea that a dwarf can flap their arms hard enough to fly, even if it takes a natural 20 followed by a natural 20 (or a 1 in 400 chance). If it just requires a nat 20, you are saying that 1 out of every 20 tries to fly by flapping arms will be successful.
If this is not something you want in your game world, then don't allow the roll. This is where questions like "are you sure you want to spend your action doing that?" can come in, or even a more blunt "flapping your arms is't going to help, would you like to try and grab hold of a branch or outcropping of rock on your way down?" Or just roll with it. The player says they flap their arms, you tell them to roll, then narrate it failing but them managing to grab and hold onto - out of sheer instinct and panic - a branch. Or their coat snags on a branch and they think they're actually keeping themselves afloat with flapping their arms.
The same is true the other way too. If you have an explosion of instant death going off, but you don't want the party to be affected by it, then you shouldn't have the party roll to outrun the explosion. Why? Well, first, the roll means there is a chance for the explosion to out run them. And chance means that someone could (and with 4-6 players rolling, someone will probably get a bad roll) get a horrible result. Now you either have a dead PC on your hands, or you need to hand waive the PC not dying which is worse than just not calling for a roll because you've also put into question whether or not future rolls are meaningful either.
In both situations the answer is to just not call for a roll. The impossible thing can't happen, because it is impossible. Ask the player what their actual goal is, and see if you can find a way for them to attain that goal without breaking the rules of the world. Accept that by not having the mega-deathball hit the players that you will lose some of the tension from that scene, but you will also reinforce with your players that when you call for the dice it will be meaningful, making future situations even more tense.