I didn't think your reasoning could get any nuttier. You surprised me.
Your claim ignores one important factor. When pigeons take off, their first move is usually to gain elevation. They usually do this for a couple seconds before acceleratign horizontally. There's no reason to believe the pigeons would be out of Rosemary Willis' field of vision by the time she looked up.
You may want to
view a slow motion video of pigeons taking off from an elevated perch. From a roof, they jump up and fly forward. From the ground, it is not so easy to fly forward because they tend to run into things - like predators and, ironically, Tesla cars. So they have to fly up first. And, by the way John, you might want to work on developing your ability to recognize a joke.