They actually did make fetch happen. Once upon a time it was usual in Javascript to use a thing called XMLHttpRequest which despite its name isn't actually for XML, it's just that XML was a big deal when it was created. The replacement API for making normal HTTP requests is just named fetch, and it was "new" so long ago that popular web browsers had versions like 40 rather than 150.

That movie is so old it's entirely possible that it's just named "fetch" because that's a reasonable thing to call this feature and so it's a coincidence, but I do like to think that at least some people at WHATWG were quoting Mean Girls...