The patient would have probably been even better if the sham surgery wasn't performed at all. Placebo effect nowadays is understood to be very small or even nonexistent, see e.g.[1][2][3]. What is actually going on is that patients most often just tend to get better with time, and this is just as true for common cold as it is for pain or injury. Researchers just confused this with some mental effect of giving placebo.

[1] - http://www.nejm.org/doi/full/10.1056/NEJM200105243442106 [2] - https://www.ncbi.nlm.nih.gov/pubmed/15257721 [3] - https://www.ncbi.nlm.nih.gov/pubmed/20091554