For instance, if they used this to "enhance" a picture with a piece of paper in someone's pocket, these letters would be enhanced based on other forms somewhere else in the picture -- so some vague letter shapes might become 'Burger King' just because the photo also contains a Burger King logo somewhere :)
Yeah, and in fact the fact that it looks crisper can be misleading. You can't rely on a detail that a method like this infers from the low resolution image. Look at the green tiles on the kitchen floor in the 6th example. The "Our SR Result" image looks fantastic, but it's obvious that it's false, because the tiles end up misshapen and unevenly spaced. You really wouldn't want to convict someone of murder based on this type of enhancement.
Statistics is not "luck", it's possibilities.
So, it might can't be "relied upon" _totally_, but, as it is automated, it can be relied upon _MORE_ than mere guessing at the fuzzy picture.
Humans are easily fooled. They will look at a fuzzy picture and see possibilities, but they will look at the output of this algorithm and see fact. There are other algorithms that predict the possibility of objects (usually letters) producing an image that are more suited for investigative work.
For example, if what you're really trying to do is decode text, this algorithm will lose every time to one that knows the prior probabilities of natural human languages. ("ONLY" is much more probable than "QNLY", but this algorithm does't know that).