The question highlights a fundamental epistemological wrangle. To presume here what should be the job of science to demonstrate, implies three successive conjectures about scavenging:
As philosopher of science Sir Karl Popper would have remarked, this chain of accomodative argument is self-servingly 'immunized' against falsification - because absence of lion bones at our cave is both explained and explained away by it. So, does Ockham's Razor mean we should forget the lions and say humans caused the elephant's carcass? Not exactly. Students of the evolutionary record know full well that absence of evidence hardly implies evidence of absence. Still, generally lower frequencies of large carnivores in Mediterranean Mousterian assemblages compared with those of northern latitudes may hint at less competition for resources, between them and humans, allowing some relaxation of selection pressure on human behavioural constraints (Gamble, 1986, 311-312).
Nevertheless, modern hunter-gatherers' behavioural débris lacks clear parallels before upper palaeolithic archaeological assemblages first appear (for instance, in middle palaeolithic ones), so any null hypothesis of modern behavioural identity seems incorrect (Binford, 1989). Null hypotheses have an important part to play in developing scientific archaeology, especially when framed as a biconditional "if x, and only if x, then y..." (Murray and Walker, 1988).
Scavenging, then, still outweighed Moustrian hunting? Well, beasts can die of disease or misfortune; from neither animal nor human predation, whilst permitting both human and animal scavenging. Perhaps it is high time that early Upper Pleistocene "biological change and behavioural change be decoupled analytically in Europe, as it has been elsewhere, so that empirical relations between these dimensions can be examined" (Simek and Price, 1990 cf. Simek and Snyder, 1988). Maybe, then, we shouldn't presume a distant Neanderthal past was diametrically different from that of humans originating in Africa. Couldn't an evolutionary, albeit truncated, trajectory of Neanderthal behaviour in western Eurasia show at least some parallels with an early Upper Pleistocene course taken by human behaviour in Africa? As Clark and Lindly (1989) have remarked, "little is to be gained by ignoring these epistemological issues. If we continue to do that, we will continue to fail to confront the fundamental ambiguity of pattern in both the archaeological and the palaeontological records. We will fail to develop a basis for making strong inferences about the past".
Still, the substantive findings from European Mousterian deposits give rise to conflicting interpretations, well-reviewed by Mellars (1996, 193-244). Clearly, where abundant big game remains in deposits permit detailed taphonomic analyses (e.g. Combe Grenal: Chase, 1986) that nevertheless allow a variety of interpretations, little can be read into our slim pickings as yet awaiting detailed taphonomical research. Some general questions seem important though. Was big-game hunting a sporadical exception, in time and space, to the Mousterian behavioural rule of scavenging, as Binford holds? Was it mainly opportunistic and unsystematic? Was any systematic Mousterian big-game hunting tightly restrained to just one or two particular species (and spatiotemporally)? Was small game hunted systematically?
A schlepp effect (Perkins and Daly, 1968) could account for carrying back to base-camps scavenged head-parts from which fat might be gleaned, so necessary as a human energy-source substituting for carbohydrates from plants unavailable in glacial winters (cf. Speth, 1987, 1990; Speth and Spielmann, 1983; cf. Stiner, 1995). Male cervid head-parts, here, might also offer useful antlers for knapping billets, during winter months - an actualistic conjecture suggested by our Cueva Negra findings. Wildfowl and other avian game species are consistent with reliance on fat during cold months by predators at Cueva Negra. Had these been mammalian or avian predators and scavengers, a great quantity of meaty (often gnawed) skeletal parts of larger mammals should have been found. Might it be more likely that humans searched out feathered game that hardly admit opportunistic capture in quantities adequate for the fat-requirements of human groups?