They may get their powers from a Divine source, but you are misunderstanding the meaning of secular. Secular means to not be ordained as a member of the clergy or as a monk. Paladins are not necessarily members of the clergy or monks. Therefore, they are secular. It's perfectly possible for someone to not be a member of a religious group and receive divine power. All it means is that either a deity favours that individual or that his commitment to an ideal or cause is so powerful that he derives divine power from it (i.e. is favoured by some sort of divine force).
I strongly recommend you reread the Paladin and Cleric (as even these do not need to be ordained) fluff in the PHB.