The natural history is unusual enough that it deserves stating without embellishment, because the embellishments are the part that gets challenged.
Communication. Elephants produce infrasonic calls below about 20 hertz, at the edge of or beneath human hearing, which travel several kilometres through air and further through the ground. They detect these partly through the feet and trunk, sensing seismic vibration. Katy Payne's identification of elephant infrasound in 1984 opened a substantial research field, and coordination between separated groups is now well documented.
The trunk contains no bone and an estimated forty thousand muscle fascicles, and functions as nose, hand, hose, snorkel and weapon. African elephants have two opposing fingers at the tip and Asian elephants one.
Death. Elephants show repeated, sustained and specific attention to the remains of their own species, investigating bones and tusks with trunk and feet, returning to them, and reacting differently to elephant bones than to those of other animals. This is well documented in the field. What is not documented, despite constant repetition, is the elephants' graveyard: there is no place elephants go to die, and the concentrations of bones that gave rise to the story are explained by drought deaths at water sources and by ivory hunting.
Memory and cognition. Long-lived matriarchs retain knowledge of distant water sources used only in severe drought, and groups led by older matriarchs survive drought better, a finding from Amboseli. Asian elephants have passed mirror self-recognition tests. The proverb about never forgetting is closer to true than most proverbs about animals, which is worth conceding rather than dismissing.