There is even a wikipedia page on it: https://en.wikipedia.org/wiki/Monkey_gland

Which still sounds super fake to me. It takes a host of modern drugs to prevent rejection when doing human-to-human transplants. I have long odds that monkey tissue would result in anything but a painful, septic death.

As a medical benchmark, penicillin was discovered in 1928.

Edit: I was ignoring the obvious - sham surgery! Just leave a bit of a scar, maybe inject them with some cocaine, and everyone comes out smiling.