I've seen this objection a few times and I'm really not sure why anyone that had COVID would be all that fussed about getting the shot. We don't know how long antibodies from having already contracted it last for, so why not get the vaccine?
If you've had COVID you are more likely to have an adverse reaction to the vaccine, it's just how the immune system reactions. If I knew I'd have 2 bad sick days to take 2 doses of a vaccine that I have already beaten.. meh.
Every single person I know who has had COVID had a bad reaction (I think I misused "adverse" there, apologies) and this seems to be the commonly accepted pattern. Regardless of whether or not it's true that's the perception.