That is exactly the point. It do in fact override prior restraint.
McCain could have published his campaign ads on his own webpage (and maybe he did).
But it just does not have the same impact as Youtube.
Google could have chosen to keep McCains videos on Youtube. But then they would loose the DCMA safe harbour proctection because they did fnot ollow the DCMA provisions.
Which could be really expensive for a big company like Google, and why would they risk that for McCain.
So in principle there is not prior restraint. In practice the provisions works just like a prior restraint.
Now DCMA is USA and for hosting and searches.
ACTA and other new initiatives expand this principle to the rest of the world and includes also ISP's and all kinds of services on the internet. I.e., the common carrier status is undermined.
Instead of introducing prior restraint you make everyone liable for every single bit that passer thought their servers, routers, software of cables. They you make exemptions based on certain criteria.
In Denmark they just proposed a new law regulating gambling. They just make ISP's, DNS-servers, etc liable for letting Danes gamble on sites, that are not registered with the danish government (and thereby paying taxes). But you are exempt from the liablity if you block access to sites when requested by the government.
It is just a loop-hole to introduce prior restraint.