Does the human visual system implement (adaptive) histogram equalization?
This isn't exactly what you are referring to, but I think provides a similar function and has been shown in vertebrate vision:

https://en.wikipedia.org/wiki/Normalization_model

Divisive normalization as a canonical computation across the brain

While this does not implement histogram equalization, I think it is actually a better-suited explanation of the checker board illusion - because local luminance and contrast normalises the activity of all neurons in the area.

Again, this doesn't quite answer your question but maybe provides an alternative computational step occurring in vertebrates?