In court, if a case is dismissed without prejudice, it means that the case could be retried in some fashion. If it is dismissed with prejudice, then it can't be retried (the plaintiff can't bring new charges or modify charges for this particular issue).
So I think what they believe it means is that signing "without prejudice" means that the signature on the contract can be revoked at anytime nulling their contractual obligations. I may be wrong of course but that's just my guess.
Not sure why they just didn't buy the house outright without a loan in the first place with this so-called "BC Trust" and make it less complicated and cheaper for their made up magic money account.
You're probably thinking too deep into this. They probably know prejudice is a bad thing, and heard the term "dismissed without prejudice" at one point, and thought that without prejudice is obviously good.
They're just vomiting legal words onto paper hoping it makes magic happen.