In my case, the phone wasn't anywhere near in hand; it was buried in an inside pocket of my coat, which I was holding by the hand that works better (remember, arm injury).  This is somewhat the crux of my question.  If the phone had been easily reachable, then I could have just pulled it out, swiped to bring up the camera, and taken a shot in the span of a few seconds...but under the actual circumstances of this situation, there's no way I could have been that fast (meaning I had to follow her to do it) or that subtle (both from the digging for the phone and, of course, following her with it after she'd passed me).