There are opposite versions of that story where the drug is a specialized 1-off custom living biological product (often a patient's own engineered immune cells). An entire company's years of effort and existence are tightly coupled to a patient's survival, and sometimes they're hundreds of miles apart.
Those plane tickets, with coolers of ice in hand, are crazy to me.
And yeah, there are those cases where batch 1 was sent 'on time' with Courier 1 who didn't realize what they had, and let it thaw. And so backup batch 2 was sent 'super-express' with Courier 2 with minutes notice.