The amount of data they generate is humongous and can be very valuable. Data scientists can go through that data can do lot of pattern matching generate interesting insights. From how your product is doing in market or even complex predictions. That sort of stuff twitter wants developer community to build not yet another twitter client.
If you want "access to the data", you can get a firehose subscription from gnip.com or datasift.com I once built an elaborate options pricer, only to find that my "access to the data" - which was basically a scraper from finance.google.com, was cut off. So I switched to finance.yahoo.com and soon enough they cut me off too! So I asked my professor and did what he told me - pay the subscription to IV ( http://www.ivolatility.com/data/historical_data.html ) and voila, the socket was instantly open and I could suck in as much data as I wanted.
http://www.readwriteweb.com/archives/twitter_to_sell_50_of_a...
The $360k price tag is not "implied", it's the actual price for access to 50% of twitter's messages (see the link I posted). 100% access can only be negotiated with Twitter itself. To be fair, from the information I could find, the cheapest plan from gnip is $500/month[1], datasift is $3000/month[2], both quickly go up. That means you can't just whip up a prototype in the weekend for some new idea anymore. This pricing probably filters out 99% of the things that could be built on it, limiting them to projects with investor backing and ready business models (which twitter itself still doesn't have).
[1] http://web.appstorm.net/how-to/social-media-how-to/gnip-the-...