You’re both right. In any other situation we’d say “ok, these are the limits between which 2 SD of the population falls, outliers will just have to deal with it

You’re both right. In any other situation we’d say “ok, these are the limits between which 2 SD of the population falls, outliers will just have to deal with it”. And that would work. Here however we can’t measure anything, so we have no idea where to place the limits, or even what the distribution looks like.