It is highly unlikely to be electrocuted by jumper cables and a 12 volt battery as human skin can resist such low voltages. Also car battery voltage is DC direct current. 12 Volt DC is too low to cause harm. A much higher voltage (over 400 V DC) is needed.
House voltage could electrocute, 110 volts AC alternating current. The jump leads shown would need to be connected to a domestic electricity outlet. This is never shown as we never know the locations. Car battery electrocution is a common script writer device.
H has no authority to relieve Reggie Mastow of duty. He would forward his information to IAD, and Mastow's superiors would make the decision on discipline.