Yes. .org is ran within the US too. So are .info, .biz, .edu, .me, .ws, and a bunch more. The problem is most of the ccTLDs are actually operated by one of three companies, all of which are based in the US.
I was checking to see if my .asia domain was safe, and found out that .info, .org, and my beloved .asia tld are operated by Afilias which, according to wikipedia, "is headquartered in Dublin".
I'm prepared to believe that wikipedia is wrong, but you'll have to prove it. with references, citations, and what not :)
The companies you are really looking for are Afilias USA, Inc and Afilias LLC. If they were really based out of Ireland, their IP space would be allocated by RIPE (Réseaux IP Européens) instead of ARIN (American Registry for Internet Numbers).
I am wondering though: Couldn't the US make similar claims on .org and .us (and .edu, .biz?) domains?