I don't believe that the whois database that NSI got from the government should be considered NSI's property. However, the US government has made a royal mess of the situation.
Several years ago I filed a claim under 5 USC 552a (the Privacy Act of 1974) over the whois database.
See http://www.cavebear.com/nsf-dns/
Unfortunately NSF, NTIA's predecessor with regard to NSI and ICANN, answered by stating that they considered the whois database to be the exlusive property of NSI.
What do do about it now? It's going to be a legal nightmare to resolve - the value of the whois databases to marketing people is enormous and they are going to fight for them - see the case between Verio and Register.com. ICANN doesn't have enough power to fix the mess created by the US government in this respect, about the most that ICANN can do is to work towards making the whois databases subject to resonable privacy and usage policies.