Here is a blogpost by Franziska Spritzler, a Low Carb dietician who found her LDL went up dramatically when following a ketogenic diet. The link above is to her results after she modified her diet, and you can follow her links back to the beginning of the problem.

I don't recall if she also took statins but she was able to allay her own fears and her doctor's by modifying what she ate. If I recall correctly, Ken (khrussva) followed her ideas and had similar good results (Ken, please correct me if I'm wrong).

Statins may be good - maybe even life savers - for some people, but they are also way overprescribed. It is up to each person to determine if the benefits outweigh the risks for their own situation.