I think you're correct. It's been a while since I read the books and I deliberately didn't reread them before the movie to avoid the kind of frustrations that occur when you see an adaptation and are too-familiar with the books so a few of these details are escaping me at present.

The Fremen in Lynch's adaptation did what they did in the book. They won the war any way they could as they were the underdogs, without taking Arakeen they couldn't win it.