That's exactly what it meant. Its use to describe UCE derived from a Monty Python sketch where a restaurant customer was trying to order food without it, but it was included in every menu item.

Technically, all proper names may be words, so yes you were/are correct in that sense. It's sort of unconventional, like saying that "Elon" is a word. The way you phrased it ("word" vs "name"), I interpreted as having a non-brand-name meaning.