Possession of an Achilles tendon is only one of the things that sets humans up for endurance running. Bramble & Lieberman (2004) note that long-distance running requires a whole suite of adaptations for skeletal strength, stabilisation, thermoregulation, and energetics. I'll summarise some of their comments here.
Skeletal strength: running places much greater stresses on the skeleton than walking does. One adaptation that reduces these stresses is an increase in the area of joint surfaces. Compared to both chimps and australopithecines, Homo skeletons have much larger joint areas in the hip joint, knee, pelvis, and lumbar vertebrae. This suggests that australopiths walked, but were not regular runners, unlike species of Homo.
Stabilisation: when someone is running, their posture is less stable than when they are walking – they tend to lean forward and the pumping action of their legs means that the torso sways from side to side. The upper body is stabilised by several features, including large spinal muscles that are anchored to the pelvis, and the very large gluteus maximus muscle. This muscle is actively involved in running, less so in walking. In addition, added stability comes from vigorously swinging the arms and thorax in opposition to the swing of legs and hips. This is made possible by a narrow, flexible waist – a feature that is fully developed in H. erectus but not the australopiths – & free-swinging shoulders.
Thermoregulation: any organism that is physically active in a hot environment will risk heat stress and must have ways of losing heat. Prolonged running places much greater demands on the body's cooling systems than walking does.
In modern humans, sweat glands permit evaporative cooling, and the reduction in body hair means that heat is more efficiently removed through convection. Obviously these don't fossilise & so we can't be certain of when they evolved. However, other features are also important in thermoregulation. One is the body's surface area relative to body mass – it is greater in tall, thin bodies (eg erectus, but not Australopithecus). Another is mouth breathing. This allows higher rates of airflow with less muscular effort than nose breathing, and also functions in shedding body heat. Modern runners are mouth breathers; the great apes are not.
Energy costs & demands: as you'll remember from the previous post, the Achilles tendon contributes to the energy efficiency of running by acting as a spring, reducing the metabolic demands on muscles. Skeletal evidence from australopith leg bones suggests that these hominins lacked an Achilles tendon and so are less likely to have been good distance runners. The arch of a human foot also acts as a spring, again contributing to energy efficiency.
Stride length is also important. Running humans increase speed by increasing the length of their stride, something which is related to the presence of 'springs' in the legs & also to having relatively long legs. Homo erectus definitely had long legs, relative to body mass – perhaps 50% longer than in Australopithecus afarensis. Longer legs do impose an energy cost, however, as they are swung to & fro. This can be reduced by having most of the leg's mass closer to the hip than the ankle (eg through reduction in the size of the foot).
Overall, it's reasonable to hypothesise that endurance running is a feature that evolved with the genus Homo, and probably in erectus. However, we need more information in order to test that hypothesis eg foot remains from erectus & more post-cranial material from habilis.
Reference: D.M. Bramble & D.E.. Lieberman (2004) Endurance running and the evolution of Homo. Nature 432: 345-352