Can refraction bend light upwards?

I was arguing with someone about this for the past few days but we couldn't reach a consensus. Basically, as we know it, refraction is the bending of light when passing through dense mediums. That's why straws look bent when placed in water and why you can see distant objects behind the supposed curvature. My opponent's claim was that the horizon was always subject to atmospheric refraction at all times that bent light downwards, creating the illusion of what we know as objects going over the horizon. His evidence was a video he linked me.

The video claims that if the sun was lower than the position of the moon but only appeared higher due to refraction, the side of the moon that is being lit by the sun should move accordingly with the true position of the sun and that because that doesn't happen that means the refraction is actually making the position of the sun lower and the true position of the sun is much higher and that's why it appears the sun sets on our flat earth. I told him that with our understanding of how the lunar phases work, that this isn't how the light side of the moon should look as demonstrated here.(doesn't work on mobile) He disagreed with me on that and the argument couldn't move any further.

As far as I am aware, and with what was taught to me in grade school science classes, was that refraction can bend objects either upwards or downwards depending on the refractive index of the medium and the angle of incidence. The reason why we can only see an extended view of the horizon sometimes is when atmospheric conditions, lighting conditions, and temperature conditions are all ideal. That's why there are so many extended horizon photos taken across a body of water usually taken at sunset.

So with so much abundance of information and demonstrations on the properties of refraction, shouldn't we be able to confirm whether it's capable of bending light upwards? I am certain I am correct in my claim that atmospheric refraction can and does bend objects upwards to view if conditions are met. What do y'all think?