Long story short, these algorithms aren't recovering information that was lost. They reconstruct the images by guessing what should've been there. So, you're not violating any information theoretic concept.
But this means the guesses can be incorrect, although the likelihood of that happening can be greatly reduced with good training data.
It tries to predict patterns from blurry shots. It might introduce artifacts that were never there: some drawings I upscaled turned distant woods into houses. You can see why this might be bad when viewing something for historical accuracy.
Sorry, I think I was unclear. What I meant is that I am familiar with these techniques, I just never heard them applied in the context of history movies.
The use of deep neural networks for this purpose seems inevitable, in hindsight.
We live in interesting times.