There is nothing to suggest he is lying about that, and its supported by Big Mum's and Kaido's initially hostile interactions(not to mention, the context was why they didn't boast about that part of their career, so it makes sense that Sengoku is being honest here). Also, while Shakky(from Sabadoy) and Whitebeard might not be a genocidal maniac, Kaido sure as hell is. Again, Kaido is a guy, who killed one of Whitebeards close buds and invaded his kingdom. I don't believe they ever had a close relationship, except for maybe Kaido's respect for Whitebeards strength. Hell, Whitebeards disdain for his Rocks members is even reflected in chapter 0 where he tells Shiki(a fellow Rocks member) to get to the point or he'll kill him. Nothing suggests the Rocks members particularly got along, and the history between them reflects that.
Whitebeard is a guy who wanted to have a family. Kaido is a guy who wants to start the biggest war the world has ever seen. Yeah, they are very conflicted with each other.