A direct cause-effect relation needs hundreds or thousands of cases in order to be established; our immune system is depressed when we suffer of depression (this is a scientific truth), which is the other side of your hypothesis. Anything we like helps to keep our mood high; almost everybody enjoys laughing, and usually also like the stimulus leading to laughing. What other circumstances were special to this person during the healing period ?

A proverb in the Holy Bible states "a merry heart doeth good like a medicine, but a broken spirit drieth the bones". (Prov. 17:22) Also another proverb says "A merry heart makes a cheerful countenance, but by sorrow of the heart the spirit is broken. (Prov. 15:13). There is a psychological phenomenon where people who have been through stressful periods will later laugh uncontrolably. I think this is a way the mind heals itself and brings a person out of the pressure they have gone through. So laugh whenever you need to and laugh often!

They have found that after some disaster where many people are injured seriously - an airplane crash for example - those that tended survive massive injuries and recovered were those with a positive attitude. Your mental outlook has a huge effect on your immediate and long-term health.