Perhaps you haven't seen this one yet: https://www.theatlantic.com/health/archive/2021/09/covid-hos...
Someone else summarized it as "Being in the hospital with covid is not the same as being in the hospital because of covid"
Someone else summarized it as "Being in the hospital with covid is not the same as being in the hospital because of covid"
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.