>>>I cannot find that acronym anywhere except in links to this story
I find your search skills, lacking :)
https://support.zen.co.uk/kb/Knowledgebase/Broadband-Understanding-REIN-and-SHINE
http://www.equicom.hu/wp-content/uploads/EXFO_anote303_Capturing-and-Analyzing-Impulse-Noise_en.pdf
https://kitz.co.uk/adsl/rein.htm
Your links are all to the UK and one in Canada. I guess my searches are U.S. centric!