I think this can all be summed up very simply. The OP asked a question based on how he thought the Touch ID sensor would operate. I think we could all agree that based on Schiller's "you don't even have to click it" comment the OP asked a perfectly valid question.
I have to disagree with those of you who are defending Schiller by pointing out that once your phone is on you don't have to click the button and therefore Schiller was right. I can't speak for everyone but I have yet to use the fingerprint scanner for a purchase, so in my case I use it 100% of the time to unlock my phone. I would guess that for everyone else it's at least 80% of the time. Basically it's safe to say the vast majority of the time the scanner is used to unlock the phone. So to defend Schiller's comment based on that logic is to say that as long as it works for a minority of instances it's ok for him to say it works for all instances.
Now I'm not saying he was intentionally misleading us. But I do think he could have explained that part better. This is really a non-issue for me but I can definitely see how a reasonable person would think exactly what the OP did based on how Schiller presented it at the Keynote.
And for what it's worth the page on Apple's website describing Touch ID does clearly explain that you must press either the home button or sleep/wake button before being able to use the Touch ID scanner if your phone was locked.
http://support.apple.com/kb/HT5883