Based on the link, it sounds like it. Although I would review the full app store review guidelines here (Note: requires you to sign in as an Apple developer). When you think about it, it makes sense though. Apple has spent a lot of time designing a unique interface and if they have, in fact, trademarked/patented that style of displaying a two-way chat, there's no way they're going to let you use it.
To be honest with you, I think it's likely more complicated than "yes you can use chat bubbles" or "no you cannot use chat bubbles." There are probably some fairly specific guidelines that define what Apple has trademarked/protected and what they haven't, hence the suggestion to make them less shiny. Long and short of it is, if you application looks exactly like the iPhone SMS application, I don't see it fairing well in the review process.