The main message of this paper is that refraction of a narrow collimated beam at a negative angle into strongly anisotropic non-magnetic crystals—a phenomenon which was observed in a number of experiments—should not be confused with negative refraction and lacks important physical characteristics of the latter. In particular, it is shown that there is no contradiction between the theory previously developed by one of the authors (in Markel 2008 Opt. Express 16 19152), where it is claimed that negative refraction is impossible, and the experiments mentioned above.