You are correct. The waitstaff in The Painted Desert and Sabatini's don't receive tips directly, so Princess instituted the surcharge ($3.50 per person if I remember correctly) essentially as a gratuity for the waitstaff. I presume that the alternative restaurants aboard MV Golden Princess will have the same surcharges.
For anybody who wants to eat in either alternative restaurant aboard MV Grand Princess, I recommend doing so for lunch rather than for dinner. I would not want to miss dinner in the main dining room aboard any Princess ship!