Interestingly, this works on my 6s when I press the home button with a finger that is registered for TouchID. I can't add a new clock when I use a different finger. That suggests that on my phone, at least, I'm really just silently unlocking the phone with Touch ID at some point in following these instructions--probably when I press the home button.

TouchID is so fast on the 6s, it's easy to unlock it without realizing you're doing it.