I have a feeling the Supreme Court would like to make a ruling that firmly reinforces the openness of court documents and legal proceedings in Canada. I'm guessing they see in this case an opportunity to prevent people with wealth and legal clout, from having a different set of rules than ordinary Canadians.
If the Supreme court were to overrule the appeals court and years of common law, they would be in fact creating new legal statutes which is the Parliaments' responsibility under our Constitution.
Because the the SCOC knows this, they will likely rule with the Appeals court, and suggest that if Parliament wants to change the way courts deal with documents, new laws should be written.
My opinion only.