An example of real life mistaken position (41:00) and its psychological pressure.
Interesting film clip, Tim, but I don't see the connection between war time Lancasters flying at 100 feet at night over all that water in fortified Holland vs. Earhart over an open ocean looking for an island.
I don't doubt the pressure as fuel ran low and Howland was not in sight - but that raises another point:
So what if she did see Gardner at that point?
While I personally, for reasons cited above, believe she would have known it wasn't Howland, she wasn't exactly going to figure out what it was and beat a path 350 miles to the NNW back to Howland, either. At that point too, it seems having found land with still having fuel aboard would come as more relief than panicking - one might gladly make the landing quite well and worry about being found later, it seems to me.
Somehow then it hardly seems like Earhart made a 'mistaken' landing at Gardner, having stumbled across it; and even had she taken it for Howland - wouldn't that itself have been a relief?
Maybe I'm just not following your line of thought on this, but these things seem reasonable in my view. YMMV, of course.