My German shepherd Lance is pretty vigilant. He has been bred to see danger and react immediately to look after the pack. He has a hair trigger and often barks and is alerted by things we are completely unaware of (mostly cats).
However he did not notice his tail catching fire! His tail was caught in a candle that initially looked safe and dog proof but turned out to be dangerous in a random freak accident.
Fortunately I noticed and frantically patted down his tail before we had a panicked 50kg German shepherd shaped fireball on our hands. Lance barely noticed.
This highlights that there are dangers and problems that however vigilant you are, they are either behind you, you have not felt them yet or they are beyond your current understanding. Therefore we need to rely on our team and the people around us, we are safer as a unit. You may be the expert in the medical situation but someone with a different perspective will see the danger before you do.