I'm pretty sure most elephants look upon these claims with skepticism.
Doubtful.
The countries that had legalized hunting had their herds grow.
The ones that outlawed hunting had their herds shrink.
That is because there was no incentive to let the elephants roam around free.
Elephants require a great deal of land and when they decide to move into a new area there is really no way to stop them. When people are already there then you have a major problem as they will destroy entire villages, crops, orchards and kill farm animals and people.
This makes elephants very unpopular and the locals support getting rid of them by any means necessary.
But with legal hunting there is a incentive to keep the elephants alive.