Last I checked, the Federal Government didn't run any of the root nameservers so I can't see any way they could be considered to belong to the US (as opposed to the private companies that own them). Not that owning the roots would mean much, since all they do is identify the (privately-owned) nameservers belonging to the various (privately-owned) registries that control the top-level domains. The only TLDs owned by the US Government (ie. the US Government operates the registries for them) are
And amusingly the politicians have it backwards: ICANN already manages IANA, the change will be to remove IANA from ICANN control and make it an independent authority in it's own right. IANA was put under ICANN control in 1998, after the death of Jon Postel who basically had been IANA up until then (a controlling authority for assigning IP address blocks, well-known port numbers, AS numbers and other technical identifiers was absolutely necessary for the Internet to function, and since nobody else was doing it Jon essentially arrogated to himself the authority to handle it).