Avoid the jet stream and trade winds. Specifically launch in the "Horse latitudes", and wait for a calm day. The very southern tip of spain is located in the horse latitudes.
The helium balloons probably didn't fall back down to earth as soon as the balloon in the story. But I still think that only 10 km seems pretty remarkable.
Good point, the rate of descent might have made a difference. This sounds like a good experiment. Let's release 10 heavy balloons (just like the ones they used) in pairs of 2 at 5 different locations around the world and track where each of them land. I'm not sure what scientific purpose this would serve but it would at least satisfy my curiosity.