I don't think you quite caught what I was getting at. I wasn't talking about how the placebo effect can cure stress but rather that stress can make people more succeptable to illness and reduce our capacity to recover from illness.
Yes, the benefits of relieving stress is a reasonably well understood physiological effect. The body's normal energy reserves can only deal with so many processes. If you are exhausted & stressed then most of your reserves are being used just to keep you going, and fewer resources are available to keep your immune system functioning optimally.
So if I have an illness that is causing me stress and a person I trust hands me a magic red sugar pill and assures me it will cure me, immediately I feel less stressed due to the belief that I will be cured.
I can't quote any studies, but I know my Dr at least believes that a reduction in stress can help the natural healing process. That's why she gives me time off work when I have ailments such as chest infections as an alternative to prescribing antibiotics.
I see what you are getting at & I agree with what you say. However the two examples you talk about here are quite different. Taking a break from work is a sensible thing to do as it frees up resources to be utilised by your immune system. You feel less stressed because you genuinely are less stressed, whereas taking a red pill is a placebo effect - you feel less stressed because you believe you are getting help.
It is possible that both will get good results, but genuine rest is usually going to be better than a red sugar pill for your immune system.