@Officina I just tried running the device with 3.3 V on Vin, and it works. At the moment, the DC in is at 2.95 V, and still running. According to the data sheet of the regulator, it goes into a bypass mode if the input voltage is too low, and that's what I wanted to confirm.
So it looks as if is more safe to run with a low Voltage on Vin.