I know people who have the ability to "see" (picture like) in their memory and read something they've read and/or written in the past (usually short term). I have seen it repeatedly demonstrated. They can do this with eyes open or closed. I'd like to know what you mean by Eidetic memory or is this just semantics we are dealing with. This article differentiates the two.
Photographic memory is the ability to recall a past scene in detail with great accuracy – just like a photograph.
www.newscientist.com
Believe me--I'm hardly an expert. But I did read a book on this last year so I have a fairly good idea I think. The two concepts are often conflated. I rarely hear people use them correctly, actually. I think even some researchers don't even bother to differentiate.
If I remember correctly, a lot of pre-pubescent kids have eidetic memories--it essentially doesn't exist in adults. It's basically the ability (short term) to recall extremely high levels of detail in something you just saw or experienced. A photographic memory has never been proven to exist outside of rumors. It would be where you could look at a page in a language you don't know and write it down word for word after. What you're describing as people "seeing" in their memory just sounds like having a good memory. Considering the rarity (or even existence) of eidetic or photographic memory in adults, I highly doubt what you saw was more than just people with strong visualization skills.
My wife knows more about this. She has pretty severe synesthesia and people assumed she had a photographic/eidetic memory as a kid, but it wasn't. She basically "sees" colors and shapes of colors for everything she experiences. She learned to read music by learning the colors in her head instead of the lines. If she's ever seen a word spelled it is extremely rare she'll spell it wrong because she can tell if the shade of the color in her head is right or wrong. She also has a weird uncanny ability to memorize recipes too.
She did well on the LSAT because she can read something and doesn't need to think about if the argument is right. Same thing for when she's reading or writing about cases in law. It isn't the right color if the argument doesn't make sense. She said she was never very good at trials because you can't say "No he's wrong because that is turquoise, orange, and forest green" in a court of law and expect people to understand you. She mostly ignores it, but some environments with really high levels of sensory input can drive her nuts. She HATES going to basketball games because there's too much going on in her head to ignore. Loud restaurants too.