According to this data, a larger proportion of the vaxx-free population is hospitalized than the vaxxed.

The problem is that incidental cases - cases where someone was hospitalized for a non-C19 reason - are included in the stats.

As I understand it, if a vaxxed person goes into the hospital for something like appendicitis, they will not be screened for C19 as part of the process because they are vaxxed. However, if a vaxx-free person is admitted for appendicitis, they are screened for C19, and if they test positive, then they are considered a vaxx-free C19 hospitalization even if they have no symptoms.