Did you read the lawyer's explanation of how it works? The deed is held as collateral against the note. The mortgage in and of itself defines the transfer of title.
Under your way of looking at the situation, what would happen to any equity that accumulated during the length of the mortgage?
Most mortgages never run their full term. Therefore, under your theory, your equity would be forfeit or go to the person who sold you the property, even if you paid every payment on time.
Sorry, but that is just not the way it works. Read the lawyer's explanation. If you search the Internet you will find multiple sources with the same explanation I cited. I could not find any to support your theory.
GLTY
CGFIA
Don't take my word for it, Do your own research! Then you will know it's true!
