Yes, it is true that elephants cannot jump, if jump refers to the state of having no feet on the ground at the same time after propelling oneself from a stationary position. The elephant's weight makes it physiologically impossible for it to do so plus the fact that the bones on its feet are more closely packed together than other mammals. Thus, they do not have the flexibility or spring mechanisms that would enable them to jump. Furthermore, elephants don't really like to have more than one foot off the ground at once.
However, the elephant is NOT the only mammal that can’t jump. Sloths, rhinoceroses and hippopotamuses also known to be non-jumping mammals. But unlike elephants, it is possible for these animals to have all four feet off the ground when they run.