My mom is a college professor, among other things, and her exams are always open book. She has every expectation of the students to have the book in front of them when taking the test.

She's a fully online professor, though, so maybe that's the difference? Different dynamic from the traditional, in-person classes professors?

I also don't think anything but her quizzes are multiple choice? Everything else is essay format, participation (discussion posts in class forum), and a HUGE paper, so there's really nothing to cheat on, aside from plagiarism, and ... there are ways of catching that.