He clearly doesn't understand the First Amendment
The First Amendment only prevent the government from unreasonably preventing someone to practice their religion or make statements in public. The only place on the internet were that would be applicable would be on government-run websites. The First Amendment would still apply after IANA is pulled out from under the DoC
Besides, its not like First Amendment rights are actually being enforced on the internet anyway, given that no one has done anything about ICANN refusing to approve the creation of .gay but just rubber-stamps applications by big corporations (and also that douche in Bellevue, Washington, USA who has registered 189+ gTLDs that have only been used by companies to protect their trademarks. One example of pointlessness: http://www.iana.org/domains/root/db/academy.html).
Also, correct me if I'm wrong, but isn't Teddy a republican, and isn't their mission to get rid of as much government regulation as possible?