All of the big silicon valley companies claim to be "flat." When I started at Yahoo!, all I heard about was how flat the organization was. Doesn't mean it's true.
The number of times a product idea was sent from an SVP to the divison VP who forwarded it to the group head of product who forwarded this with the note added "SVP wants this done by the end of the day" was more than I'd even like to think about.
