I fail to see how this is relevant. Obviously some set of people will test positive after they've been hospitalized for other causes, and another set will have mild cases that don't progress to the serious your-lungs-no-longer-work stage. The total cases and hospitalizations are still good general metrics to gauge the severity of the crisis and balance risks. If statistics didn't have nuances we wouldn't need statisticians.
Regardless, your objection is irrelevant to the comparison you've tried to make with VAERS. The COVID statistics are a sweeping accounting of common, obvious events that are easy to verify. VAERS, by contrast, is designed for hinting at the sort of literal one-in-a-millon range events that controlled medical trials can sometimes miss, where determining cause and effect is difficult. They're different tools for different jobs. Trying to apply standards from one to the other is simply spurious.
Regardless, your objection is irrelevant to the comparison you've tried to make with VAERS. The COVID statistics are a sweeping accounting of common, obvious events that are easy to verify. VAERS, by contrast, is designed for hinting at the sort of literal one-in-a-millon range events that controlled medical trials can sometimes miss, where determining cause and effect is difficult. They're different tools for different jobs. Trying to apply standards from one to the other is simply spurious.