I'm puzzled why anyone would think that, these days, IANA is under
US DoD authority. If IANA were under any US Goverment authority,
it would be NSF. But IANA is appointed by the IAB which is not
under US gov authority except to the extent that it has ties to
ISOC and ISOC is incorporated in the US.
Like most "authority" in the Internet, IANA controls the IP address
space because it is to everyone's advantage to cooperate. Anyone can
get up a machine and use any IP address they want, they will just have
a lot of trouble talking to anyone else if they don't coordinate with
IANA (or actually the registries to whom IANA has delegated almost all
the day to day coordination activities).