Are dassies really elephants closest living relative?

Yes, they are! Let me explain - about 50-60 million years ago the Proboscidea (an biological order containing one living family, the Elephantidae) evolved from mammals having approximately the size of current day pigs.

Modern scientist made morphological and biochemical tests & studies on both elephants and hyraxes (such as the rock dassie) and found out, that both species do have a lot in common. Beside all the biochemical evidences they found, the most obvious ones seem to be the similarities in the structure of the feet and teeth.

Hard to believe given the fact that the African Elephant, the largest living terrestrial animal, normally reaching 6 to 7.3 metres in length and 3 to 3.5 metres in height at the shoulder, and weighing between 6,000 to 9,000 kg and a rock dassie (weight: up to 4,7kg; length: around 55 cm) are so closely related.
btw - Manatees & Dugongs are also close relatives of elphants and dassies respectively