A couple of thoughts, looking through the dispute.
What matters is, you have a baptismal record that matches a name. It's from about the right time. How confident are you that it refers to "your" Jeanne Boucher? 50%? 80%? 20%?
You can either add the parents to her profile, and say in the biography that you're not completely sure they're correct; or you can not add them, and suggest, in the biography, that her parents names might be Pierre Boucher and Roberte Parent. Provide a link to the source, regardless.
Since she doesn't have any parents, my personal bias would be to add them, even if I was 20% sure, and just flag them as 'uncertain'. You can disconnect them later if you need to.
The argument "Both of them are also ancestors of mine and I am not ready to accept anything about my ancestors." is completely invalid. Maybe you can claim first or second hand knowledge of someone who died in 1950. For someone who lived in the 1600s, it's specious.
Also, the point is not whether one website is valid or not. What matters is the evidence they provide. So the argument "do we trust and accept Fichier origine's findings? Do we accept PRDH's results? If not, we reject all the profiles that have mentions of them." doesn't make much sense to me, either. Not when you have a copy of an actual document.