I don't think they can claim to have completed the Leith Links - Portobello route either.
The new sections are certainly to a good standard (except on the Seafield Street crossing, see threads passim). However the path over the railway bridge, and from there to the western edge of the Prom, is bumpy, too narrow, and littered with obstacles. Also the route between the western part of the prom and the central Prom is through a car park, normally chock full of vehicles, several of which are reversing in or out at any given time. Not terribly family friendly!
Sort these bits out and they can claim the route is complete.