Is that statement provably true for the previously infected? (Hint: it would be more dangerous to get a shot if you’ve already had it than to not, but it won’t

Is that statement provably true for the previously infected? (Hint: it would be more dangerous to get a shot if you’ve already had it than to not, but it won’t make Fauxi & friends any money if you don’t. Gee, I wonder why they don’t advertise that.)