Nobody says they couldn't find a time to do carving (existence of the artifact shows they could). The issue in question is comparative value of the time spent on it. Hunting, gathering and concomitant works were certainly both physically and mentally very demanding activities, and their way of life required thoughtful spending of energy. Consequently, whatever irregular pastime they had should have to be extremely valuable. It makes 'toy theory' somewhat unconvincing.
For instance, I heard Reich said in a podcast that genes linked to obesity, and diabetes, which in our times are, of course, seen as detrimental, were norm among Eurasian WHG population. And this suggests they weren't detrimental to them. Now, what would make quick fat in-body production beneficial? I guess, when your calories intake is uncertain and irregular. There are other researches on the same Kalahari Bushmen, Sahlins used to made the theory of HG affluence, which e.g. emphasize how food scarcity affects customs of food sharing. Similar observations made about "uncontacted" Amazonian tribes, where food theoretically is abundant, but the amount of time, and effort one needs to extract them with pre-metal era tools is still too high to go to rest without at least a slight feeling of hunger.
Reality is that Sahlins probably made observations in an unusually good year, and then romanticized them too much. And that's the only data point on which the theory rests to the best of my knowledge, with many points contradicting it.
One may argue that hunting with its short feedback loop, and camaraderie of a tight group relying on each other's help are healthier psychologically compared to office politics and closing boring tasks, or even farming work - not without merit. But uncertainty of survival, calorie deficit, and amount of both mental, and physical effort HG-ing required is definitely underappreciated among followers of "Original affluent society" theory. HG didn't have easy lifestyle with long creative rests. It's just something we'd love to believe, because of how cool it sounds.
There are a number of plausible explanations including just someone DID have the time and wasn't all that busy. That's even more likely but I wanted to call out the perspective that it might not have been the most typical situation that led to this.