Wrong. Fascism is very much a Leftist concept. There is no need for corporations or the wealthy to be part of government in a fascist state beyond their being nationalistic and following the government rules on participation in society. That many fascist governments practice statist capitalism or socialism comes with their being dictatorships to force rightthink within society.
To define fascism as on the Right means that the concept of Left and Right have no relative or quantitive value. The relationship, as you appear to define it, is purely subjective. That is, you put fascism on the Right because you want to, not because you can make some clear set of defined reasons it should be.
I on the other hand stick it on the Left because it is totalitarian, subsumes the individual in favor of the state, and generally has a more centrally planned economy. In my model a Fascist government would be an 7 to 9 on the government scale, an 8 or 9 on the social scale, and a 6 to 9 on the economic scale placing it firmly on the Left.