> sick, which referred specifically to a digestive upset, became a general term for any illness

This claim strikes me as dubious. (But it wouldn’t be a pop-sci article on linguistics without at least one factual error, so maybe this is it.) Wiktionary has a 15th-century attestation of sick meaning “ailing” more generally, and this accords with Germanic cognates (cf. Swedish sjuk “ill”). I would therefore suspect that some English dialects brought to America preserved the original meaning before UK English narrowed it. This claim is sourced neither in the linked article nor in the book The United States of English that it hawks. Would be interested if anyone has more on this.