Almost. When you were booking through Hyatt, the mentioned interconnect created bookings in the hotels' booking system (the bookings always had a non-Hyatt reference number, just like booking Design Hotels through Marriott). This is why honoring those reservations are easy — they are already there. As you can no longer book any SLH through Hyatt, that connection should be dead already, so the manual part happens when you cancel an existing booking.