I'm an idiot.
First, thank you all for your suggestions. Hart, we tried with and without her translucent white silicone rubber case. Pauly, we made sure our fingers sere nowhere near the lens, even holding it on the sides.
Then I read jules' suggestion. Well, of course, I removed the protective sticker. What do you think I am, some kind of idiot? I even got out a magnifying glass, looking for any edges around the phone and the lens/flash. Nothing that I could see.
Then, somewhat to my horror, I saw a small plastic tab at the bottom of the phone. You know, the kind they put on the bottom of protective films. Even though I was all alone, I sheepishly remove the film and took three photos, all with flash on. Voilà! I'm an idiot.
At least I embarrassed myself here, among friends, and not in person at an Apple store.
Thanks again, everybody!
Ken