[1] https://en.wikipedia.org/wiki/Optical_illusion#/media/File:G...
Your eyes are seeing the reflection of the sky on the distant water or fog, making it appear the horizon is closer than it really is.
So it is an optical illusion, as your brain is what is perceiving a horizon where it is not.
This particular kind of mirage ("superior mirage", as the author of the picture calls it) works the other way around: light bends away from the cold water surface. So, of I understand it correctly, the horizon appears where it really is whereas the ship appears higher up (contrary to normal mirage where the sky appears to come from the ground).
I can only recommand to check https://m.youtube.com/watch?v=er1mh90wN-k and then https://metabunk.org/refraction/
What’s also mind blowing is that the camera captures the same thing your brain is interpreting!
A mirage is not an optical illusion in the way that you describe it. The BBC correspondent is the person that called it an optical illusion, not the meteorologist. :)
It's much more related to optics than direct perception. Your brain is drawing the correct image its received, the light has just been bent so that it doesn't form an accurate representation of what you're trying to see.