So the statistics are being skewed. We don't really know by how much, because the article doesn't say how many went to the hospital for Covid-related symptoms.
The fact is it probably doesn't matter all that much. Anyway who gets to decide what is covid related or not? How do you ensure consistent application of selection criteria across teams and hospitals?
When your hospitals are filling to capacity with wheezing, coughing patients on ventilators the fact your numbers are off by a bit is by the by, and your medical staff have enough to deal with.
Anyway wouldn't this policy over-count patients who'd got vaccinated, went to hospital for an unrelated reason, but then tested positive for covid? After all, you can still catch covid if you're vaccinated, you just get to fight it off quicker. Most likely the statistical impact of all these factors isn't all that much though.