This is a dangerous subject and a controversial one. I think one of the commentators have already added that looked differently, a network can be a hierarchy and vice versa. I would add more to that, networks can be damaging too — depending on how the concept is applied and the context.
If, for example, the global economy is a complicated network, then there are some powerful nodes (say IMF etc) that impose imperial hierarchy (embargo etc) and forceful structural rebalancing on the rest of the nodes that may / not be always conducive to ‘progress’. Also, rapid, unwarranted growth of a network without such controlling nodes may not be as great of a thing as popular media will like us to believe. While Arab Spring was successful in replacing dictatorship (let us say networked effect), absence of strong hierarchy in the network of protesters created a leadership vacuum that is well expressed in NYT piece you mentioned.
What to me is more valuable are communication structures that allow rapid decision making and faster feedback without losing the context of the bigger goal — the proverbial true north. That is enabled by responsive leadership and an operating model (protocols, rules etc) which values adaptability over anything else. If hierarchies learn to adapt, they could be as good as networks.