Scott,
There's no need to confuse the terms - attacking from multiple directions isn't new. Ken's right - it takes trained and trusted troopers to do it. It's being done everyday in Iraq on the streets and has been for several years. I'm just not sure what the "new" term does other than confuse folks.
Arquilla doesn't say swarming is new. He says that the conditions are now in place for a swarming to have a strategic role rather than a purely tactical one. Doctrine.

Another point that Arquilla neglects is modularity - there's no divisional structure anymore that just plops down. Yeah, some "divisions" go with "their" brigades at the same time, but that's just due to a rotation. When units get to theater, they're broken down according to their capabilities and sub-units are attached to different commands. Both Afghanistan and Iraq are like this. 3rd BCT, 1st Cav in 06-08 was three of it's assigned battalions, a light cav squadron from the 82nd, a Stryker infantry battalion, Paladins from 3rd ACR, and an MLRS battery from Sill.
Sure. It doesn't go far enough though. The hierarchy is still prevalent, and thus susceptible to disruption from nimble enemies who have embraced the swarm as doctrine.

To get a handle on just how deep a rethink we need, and to put in tangible terms what effect integrating the swarm at a doctrinal level can hae, a quote from the article:

A networked U.S. military that knows how to swarm would have much smaller active manpower -- easily two-thirds less than the more than 2 million serving today -- but would be organized in hundreds more little units of mixed forces. The model for military intervention would be the 200 Special Forces "horse soldiers" who beat the Taliban and al Qaeda in Afghanistan late in 2001. Such teams would deploy quickly and lethally, with ample reserves for relieving "first waves" and dealing with other crises. At sea, instead of concentrating firepower in a handful of large, increasingly vulnerable supercarriers, the U.S. Navy would distribute its capabilities across many hundreds of small craft armed with very smart weapons. Given their stealth and multiple uses, submarines would stay while carriers would go. And in the air, the "wings" would reduce in size but increase in overall number, with mere handfuls of aircraft in each. Needless to say, networking means that these small pieces would still be able to join together to swarm enemies, large or small.
Which brings us to Ken's point, on which he's absolutely right. It does take a different kind of culture, particularly in regards to training. (Don Vandergriff's leading the way on that front. I'd recommend his books on the topic. )