I would say that the vast majority of players & GMs fly right in the face of the PHB, thus proving it to be completely in error.

I have never seen a paladin or cleric played who did not worship and draw power from a specific deity, and every GM I have ever known has disallowed non-religious paladins & clerics. Maybe it's just my area of England like that, and the rest of the world happily embraces the concept, but I doubt it.

This is not to attack you in any way, Matthew - I want to be very clear on that. My absolute disagreement is with the PHB, and however much I may disagree with you I absolutely respect your right to your opinion.

Technically, you are correct that according to the official rules a cleric or paladin can have no religion and be utterly secular. In practise, I really can't see many GMs allowing it.