"However, [AP] only push really big stores to the phone, which means only two or three updates a week. In my mind, that defeats the purpose of push news."

I feel exactly the opposite. The only reason I use AP is that I know I won't be interrupted, except for important stories.

Yes, I like the few interruptions as well, but I would like to take exception to your statement. As the article states, and I agree, AP Mobile will only alert us to BIG stories, not as you say IMPORTANT stories. Hearing that MJs mom got custody of the kids may be a BIG story in AP's eyes, but it sure was not important. That was one of the stories this week...
If I could selectively choose what I would get alerts for, like world news and select game scores, that would be one thing, but instead I am subjected to what AP thinks are BIG stories, which are often crappy fluff, albeit timely crappy fluff....