I think this is caused by their owner starting an animation/interaction with their pet around the same time that your active vet sim greets the owner (to start the exam with the pet).
I've noticed that the pet will wander away towards the spot on the floor where the owner was but then reroutes back to the exam table once they get to the spot on the floor. Mostly the owner will have moved to stand somewhere else.
If the owner is still standing in the same spot then the owner will interact with the pet and then the active vet sim often needs to cancel he exam and start it manually again.
Not sure if this helps any, but in a nutshell it seems like it is an animation that was started between the pet and it's owner that is causing animals to move away from the exam table and the surgery machine.
Added to the inconclusive list for now.
