A year back, I encountered a this kind of a test: binary multiple choice, one point for right answer, minus half a point for a wrong answer, zero points for no answer. (Multiple-choice exams of any kind are very rare in Finnish universities, so that's pretty much the only time in my life when I've been faced with a test like that.) Looking at the scoring, I came to the same conclusion as you: my expected score would be higher if I'd just try guessing each of the questions I wasn't sure on.

I didn't follow my own advice. I now wish I had, as I failed that exam. I was under a pretty heavy workload at the time, so I never ended up retaking it. I suspect I'd have passed if I'd just shut up and multiplied.

Why didn't I follow my own advice? I did have some kind of a conscious reason, but in retrospect it seems so flimsy that I have difficulty even formulating it here. It went something along the lines of "I might as well take all the questions I have absolutely no clue on and mark them all as 'true', which gives me a 50-50 chance to be right on each one assuming there are as many true as there are false questions. But what if the lecturer, forseeing that somebody would reason this way, wrote the questions in such a way that one alternative is more frequently correct than the other, and there isn't a 50-50 chance for all questions to be 'true'? Then my expected return calculation would be off, possibly costing me points!"

Yes, I'm aware of all the flaws in that line of thought, no need to point them out. I really didn't think it through properly. That implies that the very thing you suggest happened to your friends, happened to me - I instinctively disliked the idea, and then rationalized myself a (bad) reason not to do it.