Your lymph system relies on the movements of your skeletal muscles to push anything not water soluble through your body. This includes fats, various local inflammation signaling molecules, etc.
When you feel sick don't stay in bed, go for walks, a large part of your immune system is passive and rely on muscle contraction to work optimally.
And a common reaction to being sick is shivering, so maybe the body is already compensating for the lack of movement.
Do you have a source for this? I haven't heard this before and genuinely want to learn more about it. A cursory Google search didn't find anything related to this
https://www.mdanderson.org/publications/focused-on-health/ex....