Shouldn't it be "Twitter is building open source software"? Pointing out the obvious since most of the software companies are built on open source software but only a few build one.
I think close to 100% of the internet is built on/with open source software.
But it's a major headache to get your in house libraries/software released as open source. There's reservations because by default everything developed is considered proprietary and a trade secret. It's difficult to convince management to give stuff back and/or see a benefit, the larger the org the harder it gets. Then comes legal with the legal derp.
And finally you can't just put stuff on Github and expect it to thrive, you need resources to maintain your open source projects and again convince management beforehand that it's not just a liability.
The only one I can see is building culture/name for yourself (which I don't consider a trivial thing), but I can't think of anything else.
You probably mean this [1], but all I see is this [2]. What's wrong with me?
[1] http://www.urbandictionary.com/define.php?term=%3C3&defid=11...
[2] http://www.urbandictionary.com/define.php?term=%3C3&defid=13...
Think about this: if Twitter open sources 100% of their code, what would change? Would Twitter clones pop up all over the place? No, because Twitter is the software + infrastructure + name. Most companies think that their code contains some type of secret sauce that makes it special. In reality that's not true. Sure, Google may hide their exact PageRank algorithm, but they don't need to hide their web server code. Or their indexing algorithm. Companies like Twitter are even better for this: they do absolutely nothing that's really proprietary.
For an example of this on a much smaller scale look at TheTVDB (http://thetvdb.com/), their entire site source is OSS, yet there are no clones.
IIS is still quite widely used for many web sites. Netcraft's latest survey results suggest just slightly under 30% of all web sites are served by it. So that's some closed-source software powering a significant portion of the web, at least.
And it's quite safe to say that those IIS installations are running on some variant of Windows, which is yet another generally closed-source software system. Then there are other non-web services (DNS, FTP, and so on) handled by such Windows systems.
There are still a surprising number of proprietary UNIX systems out there in production, on the public Internet. We're talking HP-UX, AIX, UnixWare, and even BSD/OS in some cases. There are many behind the scenes, indirectly supporting web sites and other publically-accessible services.
There is a lot of other networking gear that runs proprietary software, too.
Is open source software important to the Internet? Absolutely. Is it the "100%" you're claiming? Absolutely not.
There's some high profile exceptions like the infrastructure parts you mentioned, but noone expects you to open source your router and unix config, there's nothing worth contributing and collaborating on here.