Exactly, carbon depending on the way it has been weaved and moulded can actually provide flex, the only carbon bike I had was totally rigid side to side, but it was designed to give a little up and down. And it was one of the most comfortable hardtail's I have ridden.
Like those blades they use in the Paralympics to aid running, the are made of layered carbon designed to flex in a particular direction. if they applied the same force in a different direction they would probably snap.
In a development company I used to work for we experimented with a bit of carbon moulding it was pretty interesting but making a entire bike from it must be some kind of art form.