No, that wasn’t how I understood it from the book. The original conversation was supposedly at the very early stage of Harry and Meghan dating, before she was even pregnant. Harry and Meghan themselves couldn’t even keep the story straight in the Oprah interview, because Meghan made it sound like it was linked to Archie not getting a title/security, while Harry later clarified it happened much earlier.
My understanding of the Scobie book was not that Catherine was accused of making the remark herself, but that she was allegedly in the room when the conversation took place. That is why, at first, the whole story was about “one royal.” Then after the Scobie/Dutch translation mess, it became “two royals” because Catherine was dragged into it as supposedly being present.
And if people are going to treat Scobie’s book as gospel, then they should also take Russell Myers’ book seriously, where Catherine apparently said she had nothing to do with it. You can’t just believe the book that suits your argument and ignore the one that doesn’t.
Not to mention, Harry himself later walked a lot of it back and denied that he and Meghan had accused the family of racism. So I think people have turned a messy, inconsistent story into “Catherine said something racist,” when that was never actually proven.