Total nonsense. Experiments are never falsifiable, what does that even mean? Hypotheses are falsifiable. Did any hypothesis of Milgram's suddenly become unfalsifiable one day in the last 50 years because the psychology research community found a new moral compass? Did the foundations of what is knowable by science shift during the night? "Now unfalsifiable" implies change. So what do you think changed, exactly?
You seem really hung up on a strict Popperian falsificationism that you have misunderstood.
In any case, the article mentions that you replicate a proof by reading it and checking the steps for yourself, so I feel your criticism about deductive reasoning is misplaced. It's implied that soft science papers require experiment to reproduce because they are inductive, just because the author doesn't spell this out for you doesn't mean they missed the distinction...