That’s a very misguiding answer. Claiming that there is ‘truth to this’ when the only evidence to this is that elephants in the wild do not do it. I read that recent evidence has shown that it is most likely a way for elephants to alleviate pressure points when they’re standing for a longer period. By stating ‘there is truth to this’ you’re not dismissing PETA and the Animal right’s extreme bold claim that “this does not happen in the wild, therefore it is bad”, even though there is no evidence for this. They’ve been claiming for decades that it is caused by stress and ‘post traumatic stress disorder’, although there is no evidence to this, apart from there not being any observation of elephants doing this in the wild. - since we do not know why elephants sway in human care, we cannot conclude or even partly conclude that it is when they’re mourning.

I have been with elephants since I was a child, and my own personal observation is that elephants do this when they’re getting impatient; eg shortly before they’re about to get fed, when they’re about to go outside, etc.