"We do know that the immunity after vaccination is better than the immunity after natural infection"
... is what the FDA has been saying, which seems to contradict evidence and the opinion of experts. Unless 'better' in this sentence means something other than 'more effective.'
They say 'it appears ... that natural infection provides immunity, but that immunity is seemingly not as strong and may not be as long lasting as that provided by the vaccine.'
They say that 'generally the immunity after natural infection tends to wane after about 90 days.' Also contradicts science.
It also contradicts the position of the UK and Israeli data.