This is partially true. Yes this is right, but no, the eyeballs are involved. I'm going to try describing it, but take what I say as a mostly pseudoscience explanation of the real science.

The 'visual screen' of the eyes, is where you see visualization of eyesight occur. Psychoactive drugs, such as LSD and dreams, can be seen on the this 'visual screen'.

This same 'visual screen', however, has a 2nd invisible layer, that you can see imaginarily. This 2nd layer can be seen with the eyes open or closed. The catch is that, it is imaginary, so you both can and can't see it. It's there. But it's invisible.

Without the eyes, you don't have a 'visual screen' at all, so this 2nd layer doesn't exist anywhere, thus making blind people have their mind's eye blind, too.