You've never heard of the three blind mice? I believe the farmer's wife won a Nobel prize for her work in regeneration of severed limbs.
Seriously though, the idea that mice might have a placebo effect is fascinating. I would have thought that the placebo effect would require some high-level form of self-awareness (which perhaps mice do have, I don't really know) and an understanding of at least the purpose of medicine. Maybe not though...
Edited to add: On a more serious note, I don't know if mice are susceptible to a Hawthorne-like effect http://psychology.about.com/od/hindex/g/def_hawthorn.htm Even physical science researchers have to deal with observer effects http://en.wikipedia.org/wiki/Observer_effect_%28physics%29
Edited to clean up brain-drained errors.