And the term "ketchup" came from "ke-chiap", a Chinese sauce of pickled fish and spices mixed with brine.
Besides, the idea of an Irish origin for coleslaw is spurious, as well as the idea for a Dutch origin for the term itself. The two Latin words for the key ingredients are "colis" (cabbage) and "sal" (salt). The Romans were eating vegetables tossed in either vinegar, salt water, or oil as far back as can be recorded. And all across central and eastern Europe, where cabbage was widely grown and eaten by everyone from peasants to nobility, the Roman influence was present. In addition, Genghis Khan's marauders brought fermented cabbage from Asia, which quickly took hold as well.
If one assumes that actual coleslaw is a bunch of crap thrown together with a whitish-colored binder, than an Irish origin makes sense. If one actually traces the history both of the words and of the foods, it doesn't.