From a purely mathematical point of view, as far as I'm aware, there is no difference between rotating a singular point by a phase phi, using its own location as the centre, or rotating all but the point around this particular point with phase -phi.
Yet in physics, this is not the case. Although particles are rotationally symmetric, they are very "aware" which particle is rotating and which one is not. If there were to be 2 particles, one rotating around the other particle which is stationary, changing the point of view will also switch the observation. Similarly, one could be spinning around its own point as mentioned before and the other one would be stationary, yet the observation still holds (from the right point of perspective). one could perhaps argue that there will be a force applied to only 1 particle, the one which is being rotated but can you observe that? Or am I just making a paradox for myself which by having insufficient perspective on the matter?
I'd love to hear your thoughts on the matter!
PS: I wonder if you can actually mathematically rotate a point, but since vector-fields are a thing (although in this instance discontinues), I see no big problems, although scepticism would be appropriate when dealing with 3-dimensional Dirac-delta like behaviour.
