It depends on the rule in question. Is there a viable reason to change the rule, or is it merely because the status quo doesn't suit your needs?
Allow me to provide two examples I've recently encountered:
One of my friends was claiming that his animated "dancing" tower shield should provide him total cover, where the PHB says that a tower shield can be used for cover only if you forgo your attacks. This didn't suit what he wanted the shield to do, so he said the rules are just guidelines, and to him it makes sense that standing behind the animated shield is like standing behind a door. Total cover. He didn't factor in the size of the shield nor the reach of a weapon at the extension of an arm.
Holding a tower shield on your arm isn't enough to provide total cover, it's also animated by the movement of your arm. A shield protects a defender as an obstacle obstructing a clear line of attack. The attacker has to wield the attack around/over/under the shield in order to strike the opponent, no one strikes a shield to hit their opponent. Without that free range of motion to hit, the attacker gets a penalty to hit in the form of a shield bonus to AC to the defender. The larger the obstruction, the harder it is to bypass it, thus a buckler provides a +1 shield bonus, a tower shield a +4.
No, he didn't want to have to forgo his attacks, he wanted to forgo his attacks against that one attacker and still be able to fight on the other side of the shield. A 4 foot shield is not large enough to provide total cover. If the shield were imbued with an enlarge spell effect making it one size larger, I would accept that, but changing the rule because his understanding of how a shield works...
To me, that isn't a good reason to change the rule, but to him the rules are always "just guidelines".
After some discussion, he accepted that in order for the animated shield to prevent the attacker from just attacking around the shield it would have to strategically triangulate itself to physically block the attacks with 100% proficiency, and that to get total cover he would need to crouch behind the shield like a low wall.
An example of a reasonable rule modification, is with the mending level zero spell. Some players believed that a slender dagger could have its broken blade welded back on and a severed rope mended back together. I disagreed because the topic sentence specified that the tear or break must be small. A cut/frayed rope is small but severed is not. Would you rather have a cut finger, or a severed finger? One is clearly small, severed is not. They felt that the spell specifically mentions "slender" dagger, and in his mind the blade that has broken off is a small break. If you think about it, the dagger is actually only small relative to the human holding it. Hold a pencil in your hands and apply pressure to the middle with your thumbs. You'll hear it crack. Small break. Then it'll snap. Medium break. Then it'll break in two. That's definitely a large break. The break in an object isn't relative to its size. 33% is 33% whether it's a tiny object or large.
The noun "break" is defined as a gap or an opening. Even the synonyms listed do not imply broken off or into pieces. The creators were probably well aware of the limitations of words they carefully choose. Despite this, he still insisted it was a small break and the spell should be able to mend a rope or two pieces of a slender dagger together. I disagreed.
I then pointed him to the PHB about breaking objects and damaged objects, where it says that an object that has been reduced to zero HP is ruined/destroyed. Ruined and destroyed are not words to describe small, and to sever a rope or sunder a weapon/shield, it is reduced to zero hp. I purported that if the item has any HP, it can be "healed" just as a person could be healed with a heal spell, but if the item was "dead", as a dead player, it cannot be mended but it could be "brought back to life" with the cleric spell, Make Whole.
The rope? It has 2 hp. Cut it in half doesn't destroy the rope, but it does render that one piece ruined, and now you have two new pieces each with 2 hp. Partially sever the rope, it can be mended.
By definition of the words used and the rules of the PHB, an object that has been broken off, cut in half, separated, cannot be mended. If you refer to the "bow string" argument, that string can be mended as it is still part of the bow, and the bow is in tact. The string is just a "small break" on the bow, still attached. If the bow was reduced to zero HP and cut in half, it could not be mended.
That said, an item retains full functionality so long as it has HP remaining. What if you threw the dagger, it hit the stone wall and the tip broke off? The dagger could still be used, it suffered 1hp damage, and still has 1hp left. We decided that to measure the size of the piece that broke off, that if it was less than 20% of the total size of the blade, it could be mended, but more than that would be a medium break. Although the definition stated that a "break" is a gap or opening, it was within reason to amend the rule that the mending spell could in fact weld or reattach objects that have separated from the whole provided they meet the "small" criteria.
One argument is self serving, the other is a rational conclusion. It depends on the context and rule in debate