It's not just CNN. Almost every company wants a Myspace page, twitter, facebook, blog, texting service, user accounts and registration, among other tech toys. The problem is that these tools were clearly intended to empower individuals to connect with other individuals. The companies using these things usually don't have any concerted reason to do so.
Corporations might be legal individuals, but they're not people, and they gain little to no benefit (perhaps even detriment) from attempting to employ socialisation. If you look at corporations as sociopathic, narcissistic, and single-mindedly self-interested individuals, it's clear they see these things as just another manipulation mechanism. They're not socialising; the conversation is unidirectional. They don't absorb, process, and react on the information, they gather and retransmit with absolutely no transformation. They're not talking WITH us, they're just talking AT us.
CNN doesn't do anything with the tweets. It's as useful as going to a Starbucks and having the employees stare blankly at you and repeat to you, verbatim, something a previous customer said while standing in line. "Welcome to Starbucks, Shelly said: I'll have a cafe mocha, damn I shouldn't have stopped in here, I'm gonna be late for work."
The people running companies need to realize that their company isn't one of our pals. They can't talk to us in our social circles, they can't hang out with us at a pub, and they can't sit in on our D&D sessions. They're product and service providers, nothing more. The fact that they desperately try to extend themselves into our social space borders on triggering the uncanny valley feeling.