A red herring is a false clue, something that will lead the (often detective) lead character astray, but red herrings are not intrinsically non-sequitors. The best ones will still have something to do with the plot or characters.
If we stick with Chekov and consider a literal gun, for instance, perhaps there is a red herring where one character is suspected to be the murderer because they own a firearm that matches the murder weapon. Heck, let's stick with Chekov and say that it's right there on the mantelpiece. The character who owns it is reputedly a crack shot with it and brags about his hunting prowess. Later on, the hero discovers that the gun is a replica - a fake which won't fire. He confronts the braggart, who then breaks down and begs the hero not to reveal his cowardice. Then, the explanation of where the hunting trophies really came from (since this wimp didn't do it) leads the detective onto some other clue.
In that scenario, the red herring is misleading, but not inconsequential to the plot. Chekov would likely be satisfied because his point wasn't that elements must be used a certain way, but just that everything in the story must have a point, and if you make a promise (there is a gun in this house) it must pay off (the gun gets fired (or discovered to be a fake)).