Tallest thing is implied in the show. They're pretty much spoiled teenagers on a power trip, the Control Brains do most of the government work.
No official word on the height thing, but the fact that most Irkens are around similar height with no variation raises some questions.
The whole "Membrane's wife is an alien"-thing is a uncommon ship in the fandom popularized by Bleedman's webcomic
So yeah...mostly bullshit. Still fun to think about, though.