They want to see proof that my parents, having 1) entered Canada, were 2) not settled abroad in Canada, 3) exited Canada and entered US, where I was born while they were not settled in the US, and only after that 4) became US greencard holders.
3) and 4) are simple. Simply do a FOIA/PA request with the USCIS for your parents' immigration files. The files should be able to proof that the date becoming a PR was after you are a U.S. citizen.
1) and 2) will be tricky. Do a similar request. If I am correct, CIC should send a denial to your parents saying that there is no record. That I think should be enough as your proof.