If I understood MegaLag's video correctly, Honey was indeed overriding an affiliate session cookie with their own once the user the reached the checkout. The extension would silently open a tab in the background, which seems pretty scummy. I've observed the same background tab shenanigans with the Capital One extension as well.
They do this to not interrupt the purchase flow, not to be scummy. Opening a tab in the foreground or refreshing the page is extremely annoying to users and merchants request it to be in the background so it doesn't hurt their conversion.
I never said Honey doesn't override cookies. I'm not saying this isn't a problem, it's just not a Honey-specific problem. If the affiliate networks used first-click or multi-click attribution, none of this would be an issue.