Hi Alessio,
Not in all cases. That was more of a "thought example", for example for a case with net force (like a magnet next to a steel plate). However, many cases have zero net force, but a non-zero torque (like a balanced electric motor). So, many conditions can affect the difference between evaluated torque and the cross-product of total force crossed with the lever-arm. These are all consequences of a distributed force density and whether the position w.r.t. the rotational axis is included within the integral or assumed constant to move outside the integral of force density.
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