JEEEZ...
I replace outlets all the time with the power still on.
Just never touch BOTH sides/both wires at the same time!!!!
Give the guy a break(er)!!
If you cut the power at the box, you are safe!!
BUT: if OTHER wires are also behind the box, and are covered with screw-on caps DO NOT MESS WITH THEM
Some outlets near windows etc, have the wiring back there for 220V connections (air conditioner wiring)
If you just unscrew the outlet and pull it out... the wires on it can be put on the new outlet just fine... make certain the wires go back on the same side as the original, and that the outlet is "right side up"! when you attach the wires!