Some good points--but weirdly enough, it is actually mathematically possible for (1) vaccines to have the potential to save us all and, (2) the unvaccinated to kill the vaccinated.
You can't have both of these things and an incredibly effective vaccine with high levels of sterilizing immunity. You also can't have both these things and not have the unvaccinated kill themselves at a higher rate than they kill the vaccinated.
But it's literally how the math works out. For instance, suppose the virus has R0=4, that is, if nothing is done it will spread to four other people from each person who is infected. Now suppose the vaccine makes you immune 80% of the time, but 20% of the time it doesn't. If everyone gets vaccinated, R = 4 * 0.2 = 0.8, meaning the infection dies out--you infect fewer people next round than this round. But if half of people get vaccinated, R = 4 * (0.2 + 1)/2 = 2.4, and the virus spreads widely, and most people get exposed.
Now, you still have 5x more unvaccinated people dying than vaccinated people--like I said, we're imagining that 80% of the time it worked.
But nobody would have had to die at all if everyone had gotten vaccinated, because the infection wouldn't take off...it would dwindle into nothing.
So, there you go! That belief actually isn't as crazy as it sounds. (However, whether it's true depends on what exactly the numbers are. And reality is more complicated because, well, it always is, isn't it?)