I just read it and quoted it to you. You have to read it all
in pari mutuel (all together, not just the parts you want).
I suppose that if you wanted a Paladin that didn't have Priest spells (or ignored that provision), and that didn't turn undead (or ignored that provision), and just gave to the poor (as opposed to
the church), and assumed that the other references to the Paladin's faith, or deity are just "fluff" that can be ignored, then sure!
The game is what you make of it; I am just pointing out that it takes a very creative reading of the earlier editions to come away with the impression that Paladins didn't follow a specific god, and were, instead, just general followers of LG-jerkdom.