You know, while sitting around avoiding work on a Monday, I remembered my source: some British dude living in the American Midwest talking about random words on YouTube (I think his channel is "Lost in the Pond" or something like that). The specifics he referenced were "axe/ax," "kerb/curb," and "tyre/tire." In each case, there was a settled spelling shared by British English and North American English (the latter of each pair), and for some reason England made up a new spelling or reverted to an even older spelling in the 19th century (Wikipedia source)

So I wasn't completely fabricating things, but it was much more specific than I remembered.