Cap'n Kobold
Hero
Yes, a particular piece of rules mechanics/crunch (having proficiency in heavy armour) has given paladins a common associated fluff (they are commonly heavily-armoured knights.Regardless of an individual's personal preference while walking down the street, the fact they have the proficiency on their sheet reflects the fact that they have learned how to wear it effectively at some point in the past. You still went to paladin school (or whatever), even if you make a point of looking like you hadn't.
You can't change the crunch. (Your paladin character will have heavy armour proficiency.) You can however change the fluff: your paladin might stick to light armour and thus not follow the usual paladin flavour.