Completely wrong. Canada does NOT require women to undergo invasive gynecological exams in order to immigrate. HIV is tested for by blood and HPV is not tested for at all.(Sorry this came from a drafted message)
I have a friend and she confirmed that it actually is a requirement for women older than 35 years old to get a pap smear because as they need to check for HIV or VDRL, they need to check for HPV. She did her exams in Caracas and the doctor accepted the results from a pap smear that was close to a month old.
Here is the Panel Physician Handbook: https://www.canada.ca/en/immigration-refugees-citizenship/corporate/publications-manuals/panel-members-handbook-2013.html.
Again, if a Panel physician is telling you it is required, file a complaint with the RMO.