That's true, Anolis carolinensis change his color due to stress. I can confirm that on my observations.
In cold time, frequently they display dark color if they stay in light area.
I saw and observed many Anolis carolinensis.
I saw A.caroliensis changing his color from green in gray brown, when he pass (by walking slowly), from a strong light sun area in a shadow area. No stress, no cold (was hot summer).
I saw A.caroliensis, standing in shadow and displaying more dark color. (No stress, no cold time). Sometimes displaying even very dark grey-brown color. But this is not a rule. Probably depending on light intensity.
They can rapidly change the color but sometimes the color change is gradual, slowly.
I think they use color change and for camouflage in shadow area. Not as an adaptation to the environment color, but as an adaptation to environmental light intensity. Changing from light colors to dark colors. (Of course as a reflex, not as an intent). I have not found this in the literature and I am not an expert. But I'm pretty sure they apply this strategy.
Of course it's true, light intensity can be considered a stressor,