Does flatter mean fitter?

I have been reading many articles around the topic of flat management - through a reduced number of levels from the CEO down, it should promote a leaner and more open organisation. Whilst many flat organisations are smaller in size than their larger hierarchical structure style organisations, I often wonder whether the larger ones that have many levels of hierarchy hide under performance.
I am all up for empowerment, delegation and accountability, however I wonder if a flatter management structure encourages that, impedes that, or neither...