Twitter is a social messaging platform that allows users to broadcast short messages to "followers". The web app has seen a recent explosion in growth with massive publicity surrounding celebrity usage. Ashton Kucher and Oprah are some of the biggest celebrities to recently start participating on Twitter.
Perhaps the biggest reason to doubt this rumor is that there seems to be no clear synergy between Apple and Twitter. Twitter continues to run on venture capital funding and has yet to find a revenue stream.