newtonian mechanics - Why if the torque equals zero measured from one point in space it equals zero measured from any other point?

I've heard it from two teachers and saw a task with a solution based on this assumption:

If the net torque is zero when measured from one frame of reference, it is equal to zero in all other frames of reference

This actually seems clear, especially if you put it to simple words like:

If a body doesn't rotate from one point of view, it won't start rotating if you look at it from another point of view

Still, I wanted to test it and made such an image:

I calculated the net torque measured from point A (I'll skip the designations such as $m_1, r_1, m_2$ etc. and get to the value):

$$1m\cdot1N + 5m\cdot1N - 4m\cdot1.5N = 0$$

Now, let's calculate the net torque from B:

$$-2m\cdot1N + 2m\cdot1N - 1m\cdot1.5N = -1.5Nm$$

From this it seems, that the body doesn't rotate around an axis in A, but does around the axis in B.

Answer

The sum of the torques is equal only when the sum of the forces is zero. In general the torque transfer from point A to point B is

$$\vec{M_B} = \vec{M_A} + \vec{r}_{AB} \times \vec{F} $$

you can see in your case the sum of the forces is $0.5N$, and the distance between A and B is $3m$ so the difference is $1.5 Nm$ which is what you get.

Change the downward force to $2N$ and try it again, only to see the sum of torques is the same regardless of point of consideration.

BTW: In dynamics, the sum of torque is always taken about the center of mass, in order to yield the correct angular acceleration, because the sum of forces is generally not zero.