The PACE trial on the neurological disease chronic fatigue syndrome (ME/CFS) claims that graded exercise therapy and cognitive behaviour therapy are moderately effective for treating people with CFS.
This claim is at odds with their objective findings ie people entered the trial severely ill and were still severely ill at the end of the trial. David Tuller in virology blog explains it further.
Claims for substantiation, the release of raw data has been requested from The Lancet who published to 'dodgy" papers. No answers forthcoming.

Update 2016-09-05