AKA helps making fat easy peasy...
From reading over the full text- the only really conclusive, usable and replicated clinical data I found from this study reinforces that those with fatty liver disease should avoid excess fat in their diet. The rest of the findings are in no way conclusive and the hypotheses formed, mentioned in the discussion, have more or less been abandoned since this was published in 2009. Considering this is a recent area of research (obesity and adipogenesis) that received much attention- you would think that a landmark paper such as this would be subject to further investigation. It doesn't appear to be.
The authors postulate that it may be fatty acid components such as oleic acid acting as PPAR-gamma activators and inducing the rapid adipocyte differentiation observed in their study. I'm by no means well-versed in this area- but it seems that this is a rather loose hypothesis given oleic acid has significantly lower affinity for nuclear PPAR-gamma than rosiglitazone (a thiazolidinedione-->pharmaceutical PPAR-gamma activator) however in the experimental conditions lecithin caused adipocyte differentiation about 7 times faster.
Additionally, it is mentioned that there is an early stage of adipocyte differentiation (clonal expansion) essentially circumvented when lecithin is used as the inducer. It is mentioned that this elusive mechanism requires 'clarification'. Given that there is no follow up research and that there is no related research citing this paper I would say that the correct term would be 'identification' and not 'clarification'.