They didn't "let it be set up". The internet was created to ensure their control via the chain of command. The entire point of the internet is that it's a protocol for data exchange, and therefore is platform-agnostic, in the sense that it can be run via any medium at all.
It works via radio. It works via copper phone lines. Fibre optics. Satellites. Microwave dishes. Shit, it's actually possible to implement TCP/IP by having people bang out packets of information on xylophones. Or bongo drums.
entertainment.slashdot.org/story/12/05/13/1512255/researcher-runs-ip-network-over-xylophones
So the original intention was to ensure that the US military chain of command could always get orders through, regardless of what communications infrastructure was available; if there was communications infrastructure available at all, the TCP/IP protocol could be used on it to ensure the message got through.
Now, it just so turned out that the general idea behind TCP/IP, called packet-switching, made so much sense that it was adopted widely for corporate use in telecommunications. Telcos became ISP's as this occured and the "public" internet was built as a result.
The structure of the internet itself, the protocol being widely known and disseminated, the infrastructure being re-implementable by the average joe (you can set up your own "internet" if you have two TCP/IP networks and a suitable transmission medium, eg. radio available), the structure of services such as DNS (Domain Name System), HTTP servers, etc. makes these things infinitely re-implementable by the average joe.
All you need is to know how to set it up, and the hardware and software to run it.
Hardware is cheap these days, the know-how is free if you have access to a public library, the public internet, etc. and the software is free, thanks to the Free Software Foundation, GNU, etc.
For an example of what I mean about it being "re-implementable", consider this:
There are alternate "DNS roots"; backbone-style DNS servers, that administer their own heirarchy, whilst retaining the ability to resolve outside lookups from other DNS servers. Thus, if you use the OpenNIC DNS servers, you have access not only to the regular, ICANN set of TLD's (top-level domains, such as .com, .net, .org, etc.) but also ones that are only accessible if your DNS server also resolves to the OpenNIC root-servers. Domains such as .chan, .pirate and .geek, for example, can only be accessed if your DNS settings are changed to use either the OpenNIC DNS, or one that also resolves to it (ie. a "peer" alternate DNS root, such as Emercoin, which itself hosts domains not accessible from the ICANN root, such as .bazar and .coin)
Basically, they did not "allow" it. It is a by-product of the intended feature-set/design. By this very design, "the internet" has become effectively immune to censorship.
This was made apparent to those paying attention (if they were not already aware of it) by the events surrounding The Piratebay, when all four of the original Piratebay founders were locked up in prison, the domain registrar was forced to pull the domain registration, the hosting provider was put under extreme legal pressure to deny hosting services, etc. and yet the site remained online, and does to this day, despite all (((their))) best efforts to stop it.
In short, it is simply not possible to censor the internet effectively. "The web" is only a tiny fraction of the true extent of the entire public internet, and the entire public internet is only a tiny fraction of the true extent of what is actually available to those who know where to look for it.