Should students know their reading level?

After reviewing some of my classmates responses about how they see reading implemented, I wanted to bring up a strategy from a teacher I observed in TE301. My Ct at the time had been teaching for many years and swore that students improve faster if they know the level of success they are at. She had every book in the classroom labeled with a colored sticker. This sticker would indicate a child's reading level. So lets say that there were about 5 groups and therefore 5 different color stickers used. For instance, a yellow sticker would indicate the lowest reading level. Student in this group were only allowed to read the books labeled with a yellow sticker. The teacher each week would meet with all the different color groups and listen to the read out loud. It was then that she would listen or do a running record to gage whether they can move up to the next reading level. She will show them using different books and say this is the book you are reading (bigger font, more pictures) in a few week I want you to be reading this type of book with no problem. ( smaller font, more challenging vocabulary) I struggle with this way of teaching reading for several reasons. I am not sure that all students would respond positively. Some students might shut down, and just assume reading in their "bad" subject and not try to make much effort to fix it. Other students might be embarrassed that other students know their reading level. Not to mention, the teasing and ridicule that students might face. I just feel like the risk of a stigma towards reading is far to great to approach reading groups this way. My teacher however, assured me that this was not the case and has been successful for many years. I guess it might just come down to knowing your classroom and students and what they are able to handle.