However, I think this difference between the time when I noticed that the interrupt occurred and it actuallay occured, is VERY small.
Maybe. Maybe not. Serial.print() can be very slow. Same for pulseIn(), delay(), and a number of other functions. If you don't use any slow functions, then I fail to see the need for interrupts. If you do, then there can be a significant interval between when the ISR does something (sets a flag) and when some code in loop() detect that that something happened.