After all these years of spam filter development, I still get spam regularly. I don't think there's a way to deliver news from Twitter to people in real time with more accuracy than spam filters, and that would be annoying. Again, I don't think that many people use the breaking news text messaging services that already exist and are curated by human beings.
The Twitter messages and pictures when the plane landed in the Hudson River were awesome. I didn't care that I only saw them hours after the fact. I don't think anyone else cared either. It might have been nice to get them in real time, but not at the cost of noise. Noise is impossible to reduce to a manageable level when you're text messaging people because it interrupts whatever they're doing. You could send emails instead, but then you either are still interrupting people who check their email constantly, or you're losing the real time aspect.