You're making me think about my definitions. Ex and I did five minutes in front of the JP with two witnesses, followed by lunch with the said witnesses, and I wouldn't say that we had a wedding, we just got married. Spouse and I also did the JP-and-go-for-lunch route, but we had all our families there; that felt more like a wedding.

In any case, yes, it sounds more like Annie is planning an inexpensive wedding rather than a bare-bones wedding.