Yeah, Rayleigh is completely ambiguous and that's all we can suggest, that he doesn't want to deal with all that. Shanks is ambiguous, but he's right there so it's worse.
There's a direct line. Roger was the Luffy of his time and took down the guy no one else could topple. Whitebeard was the guy who fought evenly with Roger, so Roger dying gives him his credibility. What's the best victory you can name for Mihawk? Remember that the duels with the Shanks don't list a winner, and only someone smoking bath salts would suggest that Shanks was stronger before he lost his arm.
We saw Shanks offer to fight and get declined early in the series, and he went unchallenged when he showed up at Marineford. The same place where Mihawk fought evenly with an underlying. Young Teach said that kid Shanks wasn't strong at a point where Vista was a young fighter. Shanks became a four billion berry Yonko while Vista stayed in place. So how does tying Vista give him credibility?
No gymnastics here, only questions for which I'd like an answer.