I've never noticed this... When the lights are on my bettas do not sleep, so needless to say, I have never seen their eyes when they are sleeping.
However, you may find this interesting... I have a blind Betta whose eyes are never solid black. They always have a white ring around them, and the black part in the middle glows red. I don't know if this has anything to do with him being blind.
Now that you mention it, though... I think I'll go check out all of their eyes and are if my blind bettas eyes look significantly different than the others.