That's not a credible control, because influenza and respiratory conditions are not a plausible placebo for Covid-19. The subjects knew that they are not having Covid-19, which makes them different from subjects which got Covid-19 and knew it.
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.