As someone who has had both COVID (before vaccines were available) and a COVID vaccine, this reasoning seems frankly dumb as bricks.
There is uncertainty about long-term effects of both. There is no uncertainty about the short-term effects of COVID, which are magnitudes worse than the short-term effects of a vaccine. COVID for me was a multi-week flu that scared the shit out of me because I didn't know how bad it would get or if I'd live through it. I took months to get my smell/taste back, three months to get back to previous fitness levels, hair loss, and significant mental fog and memory problems. The jab was one day of tiredness and I ran a marathon two days after no problem.
I really can't fathom how anyone could put themselves and those around them at such great risk, rather than taking a vaccine.