Okay, so what you read about is entering through the border with the US using their Records of Landing (or COPRs, depending upon when they landed). That's possible: they would have to fly to the US and then drive into Canada. (They could not take a bus, they could not take a train.) However, there is a risk that they would have their status revoked at the border, forcing them to try to enter as visitors or return home. I cannot give you odds, but it's a real risk. (I just spoke to someone this week who had his PR status revoked trying to enter Canada by car.) If they are allowed to enter, they would then have to wait two years to meet the residence requirement before applying for PR Cards. Those applications would likely be investigated because IRCC knows they were outside of Canada because of the rejected applications you mentioned.
If they just formally renounce right now, they can apply for visitor visas immediately afterwards, though they will have to demonstrate that they are not trying to immigrate, which might be hard in their situation.
I hope that clarifies things.