Both of these theories seem sound, given that I did some swaying on a hike a long time ago, both to improve my vision of an object and to calm my nerves. No bs, there I was (if I may digress, that's how many veterans start their war stories; the difference between a war story and a fairy tale is that the latter starts with "once upon a time").
So, no bs, there I was at the end of a long (12 miles) hike through the Black Rock state forest in the lower Hudson Valley. https://www.blackrockforest.org/. Like most parks there are a lot of short, heavily trafficked trails for the tourists and longer ones which the locals know - mine was longer because I started from my house and hiked 2-3 miles just to get to the park. I'm on the return trip when I casually look to my right and about 75-100 yards away in the woods is ...
A freaking African lion, female I presume, because there is no huge mane. But I can clearly see the beautiful tawny yellow-brown fur of the head and ears peaking up just above some brush looking at me. I stop dead in my tracks facing the lion. I stare at the lion. The lion stares at me. I'm telling myself that there is no way an African lion is in the woods of rural, nearly suburban, southern New York. But I can see it. But I know that it can't be an African lion. So I started shifting my position to the left and right, trying to get a better view. (I didn't want to make any sudden moves and startle it or invite it over for dinner.) Meanwhile, I'm using the time to collect my wits (not many, I know), but all I am still seeing is a lion. But the lion isn't moving.
So I take one or two small sidesteps and/or blink and I am suddenly looking at ... the butt end of a recently sawed down tree. I had looked at from just the right angle to hide the trunk of the tree, the stump was covered by shrubs and brush, and the downed crown of the tree blended into the background brush. The trunk wasn't perfectly circular, so I "saw" ears and there were some defects in the wood that I perceived as "eyes."
I cursed and laughed at myself the whole way home, thankful that I had worn my brown pants (I'll put the full joke in the Tar Pit).
On another walk in town, I saw a 10-12' foot tall extremely skinny person walking toward me. I knew he had to be really tall because the speed limit sign behind him only reached to just under his armpit. As we walked closer together, the angle of my vision changed, the speed limit sign disappeared behind the dip in the road which I knew was there, and he was just a regular guy again. No swaying that time, but I certainly slowed up just a minute when I first say this "alien."