This is an excellent question, and likely has more to do with the interaction of the nervous and immune systems than the disease itself. It’s best illustrated by the paucity of activity in extremities, for example of the rare patient previously affected by polio as a child who’s left with paralysis of a limb. This specific region will generally show reduced or minimal joint inflammation with disease onset. Another scenario is resolution following neurology insult, for example, or after a stroke. Patients will show improvement on the paralyzed side.
The reason for symmetry is therefore a reflection of the overall impact of the disease on multiple aspects of human physiology.