Before I ask this question, let me describe the set-up. You have a simple pendulum attached to the ceiling. At the bottom of the pendulum there is a sphere. The sphere rotates counterclockwise when going to the right, and then rotates clockwise while going to the left.
The question was to find what direction the net torque is on the ball with respect to to point of attachment between the sphere and the ball when the pendulum is at its max rightward displacement. Now, this is what confused me. When I learned torque, I learned that measuring torque is only meaningful (ex. you can apply $τ = Iα$ and $τ = \mathrm dL/\mathrm dt$) when you measure torque about the center of mass or a point that is fixed (not moving or moving at constant velocity).
The point of attachment is essentially in free-fall at the max rightward displacement (and is hence accelerating) and is not the center-of-mass of the ball, so from what I learned, this is an "invalid" point of taking torque (ex. you can't make assumptions on the motion of the ball from taking torque about this point). Instead of taking torque about the point of attachment, I took torque about the center point when the ball was at its max rightward displacement. From this perspective, the ball rotates from a counterclockwise direction to a clockwise direction. Therefore, from the point of the center-of-mass of the ball, the torque must be clockwise.
That was my answer, but as I said the question asked what was the torque relative to the point of attachment. The answer was
At the sphere’s maximum rightward displacement, the gravitational force (taken to act at the center of the sphere) exerts a clockwise torque about the point of attachment to the string.
I understand everything except how they took torque about the point of attachment. From my understanding, taking torque about these "non-valid" origins can lead to wrong conclusions. For example, look at this diagram of a block in space. If you take torque about point a, one will find torque to be zero and hence conclude that the object is not spinning. However, taking torque about the center of mass reveals there is a net torque and hence a change in rotation.
So, my question is, am I wrong in thinking that taking the torque about the point-of-attachment is invalid?
Credits of first picture and problem goes to AP College Board (this is a public problem you can find online)
Credits of second picture to another physics exchange user (neverneve)