Character statement made by Killer comes from the reputation that Kaido holds, which is being the strongest pirate on the seas after Edward Newgate.
This is a viewpoint the Marines also hold, as they gave him the highest bounty (as much as people like to delude themselves bounty has no relevance to strength, bounty is one of the most basic ways to judge an established character's strength, long as they've been active pirates).
So what Killer states is a viewpoint that is widely regarded in the world of One Piece, that Kaido is the strongest pirate. The previous viewpoint was Whitebeard is the strongest pirate. What this means is Kaido showcased feats to the world of one piece that no other pirate so far has done.
Is it 100% valid and applicable to all pirates? No.
Because of this man right here:
Blackbeard still hasn't actively made any major moves like the other emperors have done for decade+ now. There's no accurate way for the Marines or the world of One Piece to know where he stands in terms of strength and threat level individually. His bounty would be just be based off of him beating Marco The Phoenix (or whoever had the highest bounty out of Whitebeard commanders).
Where as Big Mom/Kaido/Shanks are all established Yonko as far as the story is concerned. So Kaido's "strongest pirate" would be applicable to Shanks & Big Mom, but not Blackbeard.. because the world is fairly ignorant on his full prowess.
It's the same with Mihawk's title, Mihawk's title would apply to people who have now been established as a certain figures in the World Of One Piece and won't be making any huge moves. It wouldn't apply to let's say..somebody like Fujitora, if Fujitora just ate his Devil Fruit and is going to be getting stronger as the series goes. But the burden of proof for being stronger would be on Fujitora and not Dracule.
Similarly right now while the hype technically does not apply to Blackbeard, it's still Blackbeard's burden to prove he's superior to Kaido. But that's not gonna stop somebody like myself from claiming Blackbeard > Kaido, because of story reasons.