How's that rumor makes sense when Mihawk never ever beat a Yonko, not even Shanks 12 years ago, didn't even fight MF Whitebeard when he wanted to see the power difference? LOL.
Zoro is literally using Oden's presence and Kinemon's technique to fight Yonko, not with Mihawk's techniques. Mihawk's training wasn't enough, he needs Oden's power instead or even Kinemon's technique.