User blog comment:AYET/AYET talks about chapter 725/@comment-101.63.16.134-20131020112602/@comment-13876472-20131020201703

Brownbeard didn't say that they are the most active pirates. He said that "whenever a major incident occured, you could be sure a pirate from the Worst Generation would be right in the centre". Also, he indeed said these five names, but the image on this panel shows more pirates of this generations.

Source: Chapter 664

I'm not trying to turn down your hypothesis. I just want prove that nothing in the text hints that "it's Drake whose causing trouble instead of Kaido". Brownbeard's words works fine with X Drake beeing an officer of Kaido.