Not quite accurate. According to your link "many teams, for strategic purposes, only carried two quarterbacks on their game-day roster." It doesn't say they can't carry a third QB as part of the 45.

>So I just learned, and posted a link to Charles. It says the reason is most teams only carry two QBs on their 45 man roster. The intent is that teams can bring in someone who has some idea about the position if the first and second stringers are injured. As you say, there is no requirement that they be injured but that clearly seems to be the intent.