"Ah yes, I aced many exams thanks to the almost infinite amounts of knowledge I picked up watching slow sweeps of dancing corporate logos and stock footage of the Grand Canyon."Just because an exam might not test you on all the information in a video doesn't mean it's not there.
You seem to focus only on certain types of information, perhaps (though you don't specify) "useful" information, but there's lots of other types.
Think of a high resolution photograph (or a frame of video) of a person wearing some clothes. With a high enough resolution you're going to see thousands or millions of fibers of cloth on the clothes they wear, the subtle gradations of color of each fiber, the direction of each tiny fold of clothing, millions of pores of their skin, gradations of color on their skin, thousands of hairs, their direction and color, and many details of the background of the image (such as, say, millions of blades of grass).
It could take volumes of books to describe all this precisely in detail. And that's just for one photo or one frame of video. You'd 30 such frames per second in a 30 FPS video, and with many of these details changing based on the lighting changes and movement of the scene in question, making for insane amounts of information for, say, a whole hour of high resolution footage.
Now, of course, you could compress this and write it out very efficiently (as is actually done in computer video file formats), but this virtually unreadable for humans.
And, of course, on the other hand, a human normally isn't going to pay attention to or be conscious of all these details in a photo or video, but that doesn't mean the information isn't there.
Humans are also going to be subconsciously influenced by or subtly affected by videos or images in ways they may not be by words -- as is clear from looking at the difference between a book and the film adaptation of the same book (nevermind that no complete, 100% faithful translation from one form to the other is possible). So the information in an image or video arguably matters even if one is not consciously aware of it.
This is all quite apart from any test one might have on the material in question. It doesn't really matter if you're not tested on the color or direction of one of a million fibers in someone's shirt, for example. Those colors and directions are still there in the image regardless.
To make the example a bit more meaningful, consider, say, Goya's The Third of May 1808[1] or Picasso's Guernica[2], or any of hundreds of other incredibly famous paintings. Entire books have been written about each of them, and that's just for one single image each. I suppose whether you would get tested on their information content would vary on the art history course you took, and its instructors, but that's almost beside the point. Arguably, these paintings contain information that can not be expressed equivalently in words (else we wouldn't need to look at the paintings at all but just read a book on them instead).
The same goes for movies, except they contain millions of images each, and not just one. So the informational content is that much greater, and is again not reduceable to something you can say in words without doing them injustic (which, of course, never stopped a movie critic, analyst, or summary writer from trying).
[1] - https://upload.wikimedia.org/wikipedia/commons/thumb/f/fd/El...
[2] - http://i.ebayimg.com/images/i/121341829928-0-1/s-l1000.jpg