Like Smerel above, I find this Sitra Achra attribution very troubling and strange. In truth, this wasn’t the only theory put forth by the Satmar Rebbe ZTL, but for some reason this is the one that kicked off.
We do find instances of the Satan creating a flash flood before the Akeida, a form of a man on a bed before the Eigel, and to mess up Iyov. All of these were tests that Hakadosh Baruch Hu was testing people, and being that it is the Satan who is the one tasked with tempting people, he was given the permission, or task, of performing the test. It is another way of saying that Hashem was testing them.
We don’t find such attribution of a long lasting favor and hospital event to the Satan, but this is the idea that is being stretched.
It is a brand new idea into Judaism not to thank Hashem for salvation but to attribute it to strength or other powers. We always took for granted that the miracle of Purim was self evident, and not just because we were told it’s a miracle done by the right Power.