Humans are hierarchical creatures, this idea has been co-opted by folks and turned into a political argument, but nevertheless in many ways humans look for someone to "drive" decision making, even in a fair and democratic organization.

If you want to go against the grain of traditional hierarchy, I don't think 'flat' is the way to go. At least not using the visualization of a horizontal, continuous line. Maybe "dash" is the way to go, with discrete, separate non-hierarchical organizations collaborating to a common end.