Have a look at
http://en.wikipedia.org/wiki/Ketogenic_diet for some information.
It is a while since I looked at this but a diet which is almost all fat can have a significant benefit for epileptics, but studies have found that it it very difficult to make this palatable. However it is a viable option.
With regards to the need for fibre, read
http://www.diagnosisdiet.com/ketosis-and-constipation/ for an alternative view.
This is just one site Googled at random - there is more information out there which questions the role of roughage in constipation.
It is dangerous to accept "everyone knows" knowledge from the Internet - even from official bodies such as NICE and Diabetes UK.
Some on this site are following the latest research papers, and are also aware of (un)intended bias built into research projects which reflect the requirements of the funding bodies. If you are selling your services in return for funding you have to pitch to your intended employer.
So people should be aware of options such as very high fat diets including those with little or no roughage.
I don't think anyone here is instructing anyone to follow a specific eating plan - just making people ware that "everyone knows that" isn't always the whole story.
