The Internet is not something that can be controlled. It is owned by the individuals who own their computers, routers, and wiring. It can be made into a completely decentralized mesh, with wireless signal bouncing from one neighbor to another across continents!
The arguement that the US is giving away a powerful weapon or anything of the sort is hilarious. ICANN didn't give the US any kind of advantage, and if we ever tried to use it in such a manner it would be downright reprehensible.
Still, I'm wary of international control over ICANN. There are many reasons to do so, and more every day due to the increasingly small minority of the internet that the US represents. Having ICANN be subject to US law, however, placed strong guarantees on free speech and expression that won't necessarily be upheld by an international organization. Depending on how much influence China and other such nations are able to garner they could certainly politicize the domain registration process and censor political speech. One can't jump to the conclusion that this will happen to what is currently a technical body, and I find it likely that principles condusive to a free and open internet will made binding when the shift does happen.
There are concerns with subjecting ICANN to international oversight, but so long as it is done with a modicum of common sense it is the right thing to do.
Whether a company owns its domain name record with the root nameserver monopoly is becoming ever less relevant as people use trusted search engines, bookmarks, and links to access their information. It is very simple to bypass the default authority and use another trusted authority instead -- and some browser plug-ins and P2P protocols do this already -- whether DNS based or otherwise.
Am I the only one who imagines the that negotiation process for this crap went something like this:
US: We pwn teh internetz!
World: We make our pwn internetz!
US: I let u has some of my internetz!
World: Rly? We can has some too?
US: No, I wuz lying. pwnt, n00b!
World: You suk!
US: Just kidding, you can rly has some of my internetz.
Us: Sure, but you gots 2 take Al Gore 2.