> it's not going to recover real details, it's just going to sharpen lines and potentially show details that look real but might not be

Super resolution as a name covers a number of techniques, but some absolutely can recover real details. Eg Superresolution from video will integrate over time, allowing sub-pixel accuracy. Imagine a grid of pixels, each of which covering a defined area of the source. Now, if that grid moves, the area covered by each pixel will be slightly different. The differences between frames can then be used to determine with accuracy a higher resolution output image.