Lets make up fake numbers to show an example of it being mathematically possible

100 people, 80 vaccinated, 20 not vaccinated

in the hospital are 15 vaccinated and 10 not vaccinated

To compare the groups you need to do math. You have to pay attention to the percentages of the groups when comparing groups of different sizes

18% of people vaccinated are in hospital

50% of people not vaccinated are in hospital

15 is bigger than 10 but the percentages show a different story.

This also doesn't take into account people who already died. If people are already dead then they can't count for those in hospital.

If 90% of one group dies quickly in the hospital then they can't possibly be counted as still sick. You'd be better off in the hospital if the other group was mostly dead instead.

TLDR: we need more numbers to make an accurate comparison