I dont understand the control they used at all.

They compared hospitalized covid patients to a random control of the general population unless I misunderstand this completely.

The covid patients are a older, more overweight, more diabetic, have more lung conditions, have more dementia cases, have more previous cancer diagnoses.

It would be incredibly surprising if you did not find this correlation.

Its like going to an ICU, look for people with yellow socks and compare those to the average american. Then conclude yellow socks have a negative health outcome because the guys in the ICU are less healthy a year later than the average american