My own suspicion is that all of those factors matter, and making blanket statements on the basis of this one case is simply bad science.
EDIT (quoted from the comments by the author) "AND MORE INFO FROM DR. MURRAY:
This particular study didn’t look at any specific fat types, but used a fairly normal mix of saturated, polyunsaturated and monounsaturated fats, as well as long chain and medium chain fatty acids. The readers are absolutely right that not all are likely to be equal, so we are carrying out further studies to flush out the real culprits. My own feeling is that the long chain fats are the worst offenders when it comes to decreasing metabolic efficiency, with medium chain fatty acids (such as those in coconut oil) possibly being less detrimental."