I'm with
@Trilt , honestly I could easily see this as a case of miscommunication. Mostly because this past spring semester our cardio prof came up to us a couple days before the exam and apologized because he knew it was going to be an online exam and thus assumed it would be open book, so he wrote more difficult questions operating under the assumption that we'd be able to go into our notes. The test wasn't open book however, and he found out late, so he essentially took the last class period before the exam to pretty much go over the exact topics he asked about on the test. So if the professors can get confused about open vs closed book, I can easily see that being translated into students being confused about it.
Granted I definitely don't know the specifics of this case, but half the class seems like far too many to be maliciously cheating...