A lot of this come from NS DMs hat require rolls for anything 'action' related or important. It's part of the that NS does not want the DM making the call on anything: they want the rules to do so. The dice and the rules say if a character does something...not the DM.
This is not my experience. DMs make calls all the time. However, if the rules say "Magic Missile always hits" then they aren't expecting the DM to suddenly ask for an attack roll when they cast the spell. And if they are sneaking, they don't expect the DM to declare "and the guards sound the alarm" without allowing you the chance to succeed.
Also, more then a few NS DMs don't have anything happen in the background that directly effects the players, and if it does the DM will immediately tell the player to make a check. And more then a few NS DMs do tell players "I will tell you when to make a check".
Well... yeah? This gets into the idea of informed decisions. To give an IRL example, I was once playing a Storm Sorcerer who was in a fight with a Dracolich. I had spent multiple rounds of combat blasting this thing to kingdom come, and at one point mentioned to a party member (because I was tracking) "We've done over 500 points of damage to this thing, it has to be close to dead." and the DM was confused on why I thought that. I mentioned that, my character alone had rolled almost 300 damage from his attacks... which is when the DM told me this was a Blue Dracolich and immune to lightning. He had never described that the dracolich had blue scales (he'd forgotten) or that it wasn't reacting to my attacks. Which turned an epic fight into a sour memory of wasting my time and energy for nothing.
Players cannot react to or notice information that is not provided by the DM. And it feels very much like a betrayal when a DM has something directly affect the Character without any knowledge, or have them automatically fail or be affected by something without a save.
At the same time, your last line refers to players who constantly interrupt to ask to make a check, and a DM who, hopefully kindly, tells them that they will let them know when that is necessary. After all, I often will give players information just for them asking a question, no check needed, because it is obvious or common knowledge. Anyone who has existed in the world will tend to recognize the holy symbol of the king of the gods, no point in making you roll religion to know that.
A lot of NS gamers feel a character can only do what is on the character sheet, or in the rules. Anything else is "wrong". Like the above, this comes back to not wanting the DM to make any calls.
Not in my experience. In my experience it is far more about reliability. My character can skin a wolf and cook its meat, don't need an ability on the character sheet. But if I have an option between using the shield bash shove from my feat, or attempting to throw a looped rope around an enemy's feet to trip them and knock them prone... I'm going to use the shield bash, because I know how it works and what it entails.
And a player who scans the skills is often not looking for a "Button" they are remembering that the game works by rolling a d20 and adding mods. They are trying to figure out what the mod is to their roll. After all, if I have a -1 charisma... my plan is likely not going to be sweet talking the guard into letting me in. That plan isn't reliable, because I can't leverage that into a success. Which stops mattering if you believe that just saying the correct things to the DM can cancel the roll. Then it doesn't matter what your modifier is, because it is irrelevant.