Picture a hungry crowd of 100 people. They will fight each other over 10 sacks of rice because without those 'low stakes' some people are going to starve and die. They can't wait for there to be a bigger prize worth struggling over because if they they'll be dead. So what looks like petty conflict from above is actually desperate struggle for survival from below.
When someone at the top of a hierarchy points to a conflict at a lower level and says it's petty and invalid, the higher-up(s) have generally made it that way and are lying about that fact to preserve or increase their power, by offering implicit bribes to whoever is willing to kick their peers on behalf of the higher-up(s). Any time such a person talks about 'the bigger picture' it's an invitation to participants in a lower-level resource conflict to defect to the hierarchy in exchange for a minor elevation in status.
My experience is that flat structures in large commercial enterprises usually reproduce stratified structures embedded within them, and they actually enhance the degree of stratification by obscuring who makes decisions and creating unassailable cliques.