Applying for National Insurance numbers when the right to remain has been granted

I have clients from the middle east who have been awarded the right to remain in the UK due to very unfortunate circumstances.
They have adult children in this country as well has grand-children, their right to remain has been granted so that they can look after 2 of their grandchildren, which has come about due to extremely unfortunate circumstances. 
They are of very ill health but have been deemed of working age. They have both been given dates of births by the Home Office both being 01/01/****.
We have applied for ESA for them both, which has put into place their applications for NINos. upon sorting out their NINo Jobcentre Plus have requested that they change their dates of births to that of 31/12/**** thus making them one year younger and therefore not eligible for their pensions for another year.
Jobcentre Plus refused to process their claims for ESA unless they agreed to this, despite the dob being 01/01 on all official documents from the Home Office and their passports (although these weren’t officially stamped by their country’s Embassy).
Has anyone ever heard of this before? Are they allowed to do this? If so, under what law/regulation, if any, are they allowed to do this?
Many thanks in advance for your advice. 

CPC/2423/2013 may be of interest. The Pension Service (wrongly in that case) erred on the side of assuming the end of the year was the d.o.b to use, to the detriment of the claimant.

Interesting - thank you. You may like to learn that we returned to Jobcentre Plus having had the DOB stamped and certified by the claimant’s country of origin’s embassy and upon this having been done Jobcentre Plus claimed that now that the date had been certified they could no longer request the change in the date of birth!
They claimed the request for the change was to prevent confusion as according to them half of the world’s population has the dob 01/01/****. What puzzled me in this case then was why hadn’t they asked for the dob to be changed to 02/01/**** in order to prevent confusion!

Thank you for your reply.

Hmm, if they only they could issue unique numbers under some sort of “national insurance” scheme, and keep track of people that way to “prevent confusion”...

Anyway, glad this was resolved quickly.