It could be that the images are set up with compression or filter on. These are the settings I am using for the BG images.
The changes I specifically make over the unity defaults ~ Filter Mode: Point(No Filter), Max Size 4096, Compression: None, and Pixels Per Unit 16 (this is just so one grid square = one square on the tileset). I also took the scale of the backgrounds and put it to 4 on X & Y to make it large compared to the game stage.