After seeing the documents, and ASSuming they are all legit, the net effect it to make SC a guarantor of the mortgage rather than a true co-borrower on the owned asset.
As you have shown, in any sort of property distribution the actual titling is not necessarily binding. But what we also saw is that until the point the judge got involved and gave SC's family access, CC's family WAS able to assert that SC's family had no right to go in there - and CC's family was keeping SC's family out until the judge told them to knock it off.
So perhaps it was a sort of "ambush" maneuver - whereby CC could take some sort of precipitous action such as, say, kicking her out, filing for divorce, murder her, etc. and he would have a period of time where he would have exclusive control and access to the house, legally enforceable, until such time as SC/her family could figure out what was going on and get in front of a judge.
In the mean time, CC would have the full legal right to do whatever he wanted - throw things out, clean things up, etc. without worry.