Truths in combat/casting spells+attribute bonuses when spellcasting

I too am confused about truths - I cannot see why they really matter as a mechanic and that most RPG systems handle the concept as traits that are role-played - but I may be mistaken - based upon reading the relevant sections a couple of times and to my eye they look like either:

Information that is the word version of stats/abilities/skills/background flavour for characters (PC or NPC) - so having a Character Truth of “Deadeye” would mean that statistically the character was accurate or if their stats were not such that they were accurate it is just fluff and does not affect the resolution of events, but is a role-played trait like any other system. In other systems this may be strengths and weakness perhaps - so afraid of snakes or claustrophobic, again something that is either leveraged by the player of DM as a matter of course for flavour and character performance in other systems…

Or it describes a part of the world in some way that needs concrete definition. Although why this needs to be abstracted into a mechanic I don’t understand either - so for instance “a tough wall”. So that when the player(s) decide to use the nearby pickaxe it can be broken through but slowly - as it is true that it is hard to break. Again something which is just usually handled by the DM’s discretion and desire to make the play actions and outcomes make sense rather than called out as explicit player/DM facing facts.

I may be missing the point, but it looks like truths could be ignored systemically and such nuances handled by DM and player roleplaying?

Please correct me or help me see what I am missing here…

sTeVE