Tomay-to/Tomato, you've just said what I said in a slightly different way. But I'm not sure I understand - you make the case for Chaos excellently, I mean you obviously know your stuff, but then say you don't understand the use of the term false?
"From their point of view, they are basically the people of the French Revolution. Fighting because they think their leaders sucked. But that doesn't invalidate the French Aristocracy.
So again...False...doesn't make any sense."
But that's exactly what it does. It depends on your political view. For example: if you're a royalist, you believe in the Royal Family, if you're a communist then you believe in all men are equal (let's not get into which is right here, just in layman's terms what they mean). Thus to Communists, the Royal Family do not represent what they consider to be 'correct' 'just' or 'fair' rule, they are not legitimate leaders as the communists do not believe in their rule nor the rule of law that entitles them to such power, thus, they are false rulers.
So the Imperium have their governing (corpse) body, but Chaos believe that Horus - whether by might, force of conquest, by the inept rule of the Emperor, whatever, it doesn't matter - was the rightful Emperor of mankind. Thus, the current Emperor is false.
For the purposes of this discussion, it doesn't matter why Chaos believe in Horus, but that they simply do, and that is why the Emperor is false, because to them he is not the rightful leader.
Also, remember that many different viewpoints have their own valid logic and evidence, and people believe what is suited to them. Does this make other viewpoints inferior? That's a much deeper discussion.
The point is very simple for Chaos and I think you're over complicating it with 'validity of rule' and so on. It comes down to this: Chaos follow Horus, they believe he is the rightful leader. Therefore, the current leader of mankind is false.
It's that simple. GW isn't going into huge debates of political power for the purposes of a gameplay narrative, which is where the term was first used, way before the current Black Library novels explored the Horus Heresy.