Neural Network - distinguishing between several normalized values is impossible?
The math you are talking about is in equation (7):


  Let x′ be a new data point obtained by re-scaling x by δ. Then we have,
  
  
  It is easy to see re-scaling individual data points does not change
  the model’s prediction under layer normalization. Similar to the
  re-centering of the weight matrix in layer normalization, we can also
  show that batch normalization is invariant to re-centering of the
  dataset.


It proves that the prediction over x' would be the same as in x. So what you say is right, they are indistinguishable.

And I think this is what we want because improves generalization in predictions! 

For example in image classification, you are trying to detect orangutangs, if an image  I represent an orangutang, ( I x 5)+2 still is an orangutang!