My understanding is that they were in an older version of Google Maps, where you could load the custom POIs from My Maps.
But they removed it in more recent versions of Google Maps app.
They have new engines for Google Maps and My Places now. There's probably some incompatibility now in the backends for both products.
It used to be that you could look up some place in Desktop Google Maps and then right-click it and save to a new or existing My Maps. You can't do that any more.
You have to first create a custom My Maps, search for a spot and then add it from within Mapsengine, which is different than Google Maps. This change makes adding POIs in My Maps much more work than it used to be before.
Why they wanted to change the underlying engines is a mystery. Maybe these new engines make it easier to data mine or advertise. Or maybe some new exec. wanted to give both products facelifts, so that he could burnish his resume.
You can now search in Desktop Google Maps and then star the POIs you want. Then you will be able to access those starred locations in the mobile apps for navigation. Only problem with that is there's no way to organize the starred POIs or separate them for different cities or countries. That means over time, you can have dozens of these and you'll have to scroll through them on your device. So you have no choicer but to un-star them, to keep your POIs list manageable.
That is essentially the same problem with OS X Maps and iOS Maps and their bookmarks. Again, you can search and bookmark a lot of POIs on the desktop and access them later on the mobile device but you can't really organize them easily.