Their control group was people that had influenza and other respiratory conditions in the same timeframe. The hazard ratios for COVID survivors (over influenza or others) were in the 1-2% range. Meh.
What you want to control for is the lockdown effects or general disease stress, not covid-19 itself. That's what you're trying to measure.
Those aware they had Covid19 will fear all the known-unknowns around Covid19. Those who don't think they had it wouldn't have stressed about it at all.