Proof of a conjecture of Kulakova et al. related to the sl2 weight system

In this article, we show that a conjecture raised in Kulakova et al. (2013), which regards the coefficient of the highest term when we evaluate the sl2 weight system on the projection of a diagram to primitive elements, is a consequence of the Melvin-Morton-Rozansky conjecture, proved in Bar-Natan and Garoufalidis (1996).