Did you actually read what I wrote? There are a number of studies that prove that headgear reduces injuries. It also accords with the basic rules of physics. It is the same principle as to why cars have crumple zones to absorb impact.
Stop writing something that is incorrect. It could encourage anybody reading this to stop using head protection.
Here is one article outlining the science in relation to helmets. Headgear is no different, although obviously it will offer less protection than a helmet.
http://www.ncbi.nlm.nih.gov/pubmed/11388933
There are literally hundreds of studies showing why head protection works.