Yes, the animals are trained. They are Thai elephants who are unemployed since the logging industry has been severely cut back in Thailand. There are 3000 unemployed elephants, and some of them are trained to create these paintings to raise money to keep the elephants from having to beg, or God forbid, from having to be put down.
Thai elephant owners are notorious for their love and respect for their animals. They interact and play with them regularly and treat them as members of their families. While I don't know anything about the training methods they use, I'm going to hazard a guess that they are considerably more humane than those used in America, which are barbaric to say the very, very least.
Elephants have no equal in their intelligence. They do have a sense of "self," which was previously thought to be a human province exclusively. They do grieve for their dead, and for dead elephants whom they do not know. They care for each other and exhibit a degree of emotion not to be found anywhere else, among any other animal save humans, and humans, IMO, sometimes don't deserve the gifts we've been given.
So yes, this is a learned behavior, but that elephant paints better than I do. Way better than I ever could hope to. So learned behavior or not, it's mind-blowing.
Here's a link to where you can learn more about these elephants, and buy some of their work to help their cause:
www.exoticworldgifts.com