The bottom line is that if you put the disc in on day one, you will be able to play the game; but if you want to finish the career mode, you will need to connect at some point to download the cars and tracks necessary to do so. If you just want to play the game on day one, you do not need to connect it to Xbox Live.
It is all a bit confusing, but the reality is that if you want to get the most out of the game you need to connect it to Xbox Live at some point. We don’t think this is a big deal, and we suspect that most Forza 5 players understand this. The majority of the content for the game is on the disc, but Forza has always downloaded additional content.