Here is what I believe the author of that video was trying to get at. Consider the following:
If you have a grasshopper that is ten feet away and that grasshopper jumps directly over you, it takes that grasshopper ten seconds to get to a position ten feet directly behind you.
Total distance (circle with a radius of 10 / 2) = 31.415 ft in 10 seconds
If that grasshopper is now one hundred feet away, and that grasshopper jumps directly over you, to get to a position 100 feet behind you at ten seconds, it would now be:
Total distance (circle with a radius of 100 / 2) = 314.1595 ft in 10 seconds
Now, clearly the second example is going much further through space. Yet, at the five second mark, both examples are going to be directly over the observer. At the 2.5 second mark and at the 7.5 second mark, both examples would also be in similar positions around the observer.
If the grasshopper were just a point in space, and it was ambiguous how far away it was from the observer, then the observer would not be able to tell the difference. The reason you wouldn't be able to tell a difference is because its a larger circle around the observer, and the positions would line up. Circles can behave in this way.
The author of the video is implying this, but on a horizontal circular basis instead of a perfectly vertical one.
As an aside, from what I've read, I actually do believe that the sun changes speed throughout the year somewhat, but it isn't extreme.