The results
The doctor told her that her collarbone was seriously bruised and strained. Yes, it was true that some inches had been added to her neck, but all the rings were stretching her skin and muscles. They were not permanently altering her body in any way. It was just an illusion.
The difference between her and the Kayan Lahwi people was that they started this process when they were very little, so as their bones developed, they grew up deformed with the weight of the rings. Sydney just put the rings on later in life, when she was full-grown, so they changed nothing.