Fate is admittedly an acquired taste. Interestingly, my players don't mind facing off against powerful enemies with stunts and skills that they themselves could not gain any time soon (full immunity against bullets or fire, immortality, and so on).
However, what has sparked a debate is the use of stress and consequences through narrative impetus. I know that the rules explicitly state that consequences may also just appear as a result of a failed action – a twisted ankle from failing to climb over a wall, shards of glass in the hand from smashing through a window – but my players are not buying that.
The main response to this question has been "then what do we have stress boxes for?", implying that stress boxes are essentially Health Points. I tried explaining that stress boxes don't outright translate to health, as they are effectively narrative 'character shield', but again, that distinction is not getting through.
I've also thought about my motivation for avoiding stress boxes in certain situations – and that's to keep the narrative flowing, plain and simple. Yes, that may sometimes be to the detriment of the player characters, but it should never be to the detriment of the players. Someone in an answer on here wrote that "Fate is about players conspiring with the GM against their characters", but in this particular case I feel like the general understanding is that the GM (me) is trying to bullsh*t the player characters into failing.
What is the best way of dealing with this? Is there a more in-depth explanation of what stress tracks ARE and AREN'T supposed to do?
I'd greatly appreciate any input!
Bypassing stress in the situations you mentionned is playing by the rules. But don't take my word for it, let's see what Fate Core tells us.
When to use stress?
So you need to be in a Conflict for stress to be relevant, at least for physical and mental stress, which by default go away after a conflict (FC 160). And what's a conflict?
So stress isn't really an appropriate effect for a failed roll outside of a conflict where there's harmful intent, especially since the stress goes away after the scene by default. That is, unless you're using stress to model something else than the default, for example Wealth stress that occurs over longer times, and might take more than a scene or even a session to clear. (Toolkit 69)
What is the appropriate setback for a "situational" failure?
You can go with a Consequence, but it might be harsh depending on the failure, and is usually reserved for conflicts like stress. When you give someone a Consequence for a failed roll, it means that the character is sufficiently threatened to risk being Taken out. Is that what's appropriate? It might be, for example after a long fall off a cliff.
But if that's not the intended effect, consider creating an Aspect instead. It can be a negative one you put on the character, which adversaries can invoke once freely to make his life difficult, or it can be an additional obstacle in the scene (or a future one). In other words, treat it like a failed Create Advantage:
That way you can have lasting "consequences" outside of conflicts, and your players don't feel cheated.