I don't think this is incompatible with public health policy even if public health policy treats previously-infected people the same way as never-infected peopl

I don't think this is incompatible with public health policy even if public health policy treats previously-infected people the same way as never-infected people. Owing to the dramatic risk asymmetry between vaccine and disease, it's probably better to implement a policy that optimizes more for expediency, simplicity (fewer rules and fewer exceptions) and, in this case, minimizing the number of false assumptions made about the status of individuals. ie.: in the context of vaccination it's sometimes better to not assume that everyone who claims to have been previously infected was actually infected, even if we have lab data to back up this assumption. I'm not saying current policies all make perfect sense or anything, but it doesn't particularly surprise me that everyone is being accounted for in the same way WRT the vaccine.