That paladins have three spell slots at fourth level, is a reflection of the true capacity for someone with this specific training and experience, to cast spells. It is both fluff and crunch. It is the same sentence written in two different languages.That paladins have three spell slots at fourth level is crunch. That those paladin spells are granted by a god is fluff.
That paladins gain the Heavy Armour proficiency is crunch. That paladins are heavily armoured knights is fluff.
The tenets of the Devotion paladin are crunch. That paladins stand for goodness and justice is fluff.
Changing the crunch is house rules. Changing the fluff is not house rules, or home brew, or deviating from the rules. Just re-fluffing.
That paladins learn to wear heavy armor, which is represented by heavy armor proficiency, is both fluff and crunch.
That a paladin will follow a specified code of conduct is both fluff and crunch.
Changing the connection between a given piece of fluff, and its corresponding crunch, requires a house rule. You're changing how the game works. (Not that there's anything wrong with that, but it's a matter for the DM to handle.)
Inventing your own crunch, to represent fluff that is otherwise not present in the book, is just home-brewing. You're adding stuff to the game. (Not that there's anything wrong with that, either, but it's also a matter for the DM to handle.)