Finer grained is better, yes. But I don't think that this supports the idea that anyone "pretends that immunity due to prior infection is due to the vaccine."
Yes it does. Just replace the vaccine with snake oil and follow it to its logical conclusions.
I'll use some BS numbers to make the point. Let's assume: study population of 100, 20% of the population had a prior infection, half are given the snake oil.
Starting conditions:
1. Never infected, Never Snaked: 40
2. Prior infected, Never Snaked:10
3. Never infected, Snaked: 40
4. Prior infected, Snaked: 10
Now let's assume wave 2 happens. 20% of the never infected gets infected, and 0% of the previously infected get reinfected.
Both groups 1+2 combined and 3+4 combined have an average infection rate of 16% for wave 2. The groups are equal because snake oil is bullshit.
What the Ars author was suggesting is to compare group 1 with group 3+4 combined. Now you have a 20% infection rate vs a 16% infection rate. The snake oil appears to have an (20-16)/20 = 25% effectiveness just by including previously acquired immunity.
