I am no senior here in this forum but here is my 2-cent
Not all IRCC employees advised you correctly or appropriately. They also made mistakes often too. This is known facts
The Unique Client ID is something that is attached to you and you only on all Canada government-issued paperworks. It appears on your Visitor visa, your PR card and later, your Citizenship certificate.
I would go with the UCI number, instead of the one on the back.
By the way, after checking the info on the IRCC website about PGP again, this is the number on the PR that IRCC wants:
https://www.cic.gc.ca/english/helpcentre/answer.asp?qnum=1446&top=14#pr-card
Not sure why they told you about the back-top of the card!?