That is just false, the reason Sanji made this decision is because he knew that if he doesn't go with Bege BM and his Family would be after the SH and they had already started a War on Kaido, it is one of the few things that show Zoro and Sanji are thinking alike when it comes to the Crew which is to keep them out of harms way, Sanji knew his Family thus he understood the best way to keep the trouble out of their way when facing Kaido is that he should just leave so BM and his family don't follow, while Zoro was thinking it is a stupid thing to get involved with another Yonko - probably thinking that if Sanji didn't go they would be okay - when they are going up against Kaido so he though it was stupid that Sanji left.
both of them cared about the upcoming battle so Sanji knowing his family and their affiliation left while Zoro not knowing Sanji's disgusting family though it was stupid he left but Sanji was doing what he believed was best