The inclusion of animal bones in Graves I and VIII is notable. With the exception of an extensive midden, large, complete animal bones are rare from all contexts at ‘Uyun al-Hammam, and horn cores and antler are virtually unknown. Yet Grave I included the fox skull and humerus, the patella from an aurochs, and the remains of gazelle, deer, tortoise, and a notable variety of other species for such a small context (Table 3). Grave VIII contained the fox skeleton, along with red deer antler, a horn core fragment from a wild goat (Capra sp.), and other isolated bones. In addition to the disarticulated tortoise carapace fragments recovered from Grave I, the articulated remains of two partial tortoise carapaces were found beside a large cobble near the northwest portion of Grave VIII. Although we cannot clearly associate the tortoise carapaces with Grave VIII (Figure 3), articulated tortoise remains are not found in any other contexts at the site.
The press is focusing on the theory that the fox was a pet of some sort, with headlines like "fox was man's first best friend." That's the interpretation that the authors clearly prefer. As the article points out, however, there are lots of reasons that animals can be buried with humans, and fox bones are not uncommon additions to human burials throughout the Middle Eastern Epipaleolithic and Pre-Pottery Neolithic, although they are usually disarticulated. Fox remains are common in many Neolithic sites in non-burial contexts, often as one of the main sources of bone bead material, and presumably they were hunted for their pelts.
Personally, I don't find the pet hypothesis all that convincing, just as I don't believe the gazelle or tortoise found in the burials had a close and personal relationship with the deceased. It's possible, but it seems more likely that the fox was an important part of mortuary symbolism in the Epipaleolithic. That doesn't preclude a personal relationship with the deceased, but it doesn't assume one, either. We interact with animals on so many different levels, not just as pets or as prey. The symbolic meaning and ritual role of animals can be incredibly difficult to understand, but this is one case where the symbolism and context of the human-animal interaction seems relatively constant and clear.