The ISS accelerometers meassure zero. Because all the components are subjected to exactly the same forces. An accelerometer can only measure the difference in the forces applied to different parts of the accelerometer. Typically an accelerometer uses 2 major components, a 'fixed' body and a sprung mass. The acceleration is calculated as the difference in location between the body and the sprung mass. If both of them are subjected to the same force then they don't sense any acceleration.
Now lets see if you can extend that with a bit more intelligence than Paul. Assuming you and the accelerometer are in the same reference frame, can you be accelerating if the accelerometer measures zero?
Hint: You probably don't need it but you correctly identified all the forces must sum to zero for the accelerometer to read zero.
What is the classical physics name of this law?
Extension Hint: If we wan't to go deeper with classical physics you are probably going to have to break into linear and non-linear acceleration types and introduce the concept of fictional forces.
