Internet access is not a human right. He is profoundly wrong.
The gist of his argument is that the Internet is just technology. It’s how we use this technology (for things like speech) that is the human right, not the technology itself. That’s the wrong way to look at it. New technology adds new complications that require clarification.
That's what happened with the printing press. Our founding fathers chose to enshrine technology in our Bill of Rights, by saying that “Congress shall pass no law abridging the freedom of the printing press”. The invention of the printing press revealed new rights, new concerns nobody cared about until the printing press appeared. It's difficult trying to list these new rights without reference to the technology that enabled them. Instead of "right to publish", it's just easier to simply say "right to printing-press".
Vint Cerf says "It is a mistake to place any particular technology in this exalted category [human rights], since over time we will end up valuing the wrong things". The printing press disproves this -- even though actual printing presses are certainly becoming obsolete, the values they revealed are not.
You might be tempted to apply Cerf’s argument’s the printing press, and say that “freedom of speech” already covers “freedom of the printing press”, but you’d be wrong. As history has shown, it’s not always clear how to map one right onto the other. Reasons why governments restrict speech are different from the reasons why governments restrict presses. The type of restriction against speakers at crowded protests are very different than the restrictions against printed agitprop pamphlets. Governments can restrict the printing press without, technically, infringing speech.
For example, government originally licensed printing presses. The reason was that the press introduced new economics. It cost a lot to setup the press for the first copy, but subsequent copies were very cheap. You could only pay back the original investment if you could sell a lot of copies. If two printers decided to print the same thing at the same time, then neither could recoup their initial investment, and both would go bankrupt. Therefore, some coordination by the government was “needed”. This was the situation before 1709 in England. The abuse of that system, such as government censorship, forced the laws to change (“Statute of Anne”).
You might point out that the First Ammendment actually said only “press” and not “printing press” (correct) and argue that it therefore only referred to newspapers (wrong). By “press” it meant all actions of the printing press, including printing things like the Thomas Paine’s Common Sense or the Declaration of Independence. The First Ammendment very much refers to the situation 100 years earlier when the English government controlled the printing presses.
Update: Eugene Volokh has a great discussion of this here (summarized here). Samuel Johnson's 1755 dictionary makes no mention of the newspaper industry when defining "press". It wasn't until after the First Ammendment was written that "press" started to be used for "newspaper industry".
We have the same situation today, where today’s copyright laws are used to stifle freedom of expression. For example, #Anonymous hackers created a “mashup" video of Tom Cruise effusively praising Scientology. Scientologists exploited copyright law in order to take the video off the Internet in order to suppress legitimate criticism.
A simple statement of “rights” would do much to clarify things. Today, the SOPA law (designed to protect copyright) is not unconstitutional. Now consider a “right” that says “Government shall not abridge access to the Internet”. Suddenly, this proposed SOPA law is obviously wrong, because “abridging access to the Internet” is precisely what it does. It's not just copyright abuse, but issues from cyberwar to cyberbullying to regulation of Terms of Service to privacy: a clarification of rights is important.
Or consider phrasing it as "Government shall not abridge access to information". It's a minor change, removing the reference to technology. It introduces a new right, "information", that we didn't know we needed until the Internet came along (much how the printing press introduced rights we didn't know we needed). Information is every much as important as speech. But referencing the technology is easier: it gives us this new right, as well as resolves the complications with existing rights. If Vint Cerf followers convinced me I'm wrong, and that Internet (or cyberspace) is not a right, I would still insist that unrestricted access to information is a fundamental right that needs to be enumerated.
We can measure the importance of Internet-as-right in the inverse, in proportion to the efforts repressive governments take to restrict access to the Internet. Take China, for example. Their "Great Firewall of China" blocks large parts of the Internet. They force Google to remove items from its search results, such as any mention of the Tienanmen Square uprising, or even references to the recent Arab Spring (in case it's citizens get any wrong ideas). It's not speech being repressed here so much as access to information. In both repressive and free countries, we now see more attacks on Internet access than we do on speech, religion, or newspapers.
Vint Cerf is correct in saying that we need no clarification to know that the Egyptian Internet cutoff (to silence protests) was evil. Be he is incorrect in saying no clarification is needed. The First Amendment is not technology neutral, the 18th century version calls out the technology of the printing press, and the 21st century version should call out the technology of the Internet. Internet access is a human right, and even well-meaning governments are already infringing it, because of the lack of clarification.