Actually that happens much more often on the right, at least in the USA, where everyone a tiny bit less rightist is incorrectly labeled a leftist.
The true right-left axis is closely tied to the ownership of the means of production (ownership including decision-making and wealth extracting). Along this axis the right being ownership by few (oligarchy), or ownership by the financial capital (capitalism), while left being ownership by all the people (comunism) or ownership by the labour capital (socialism). So, a center would be something like the German system, a capitalist society where employees have some seats in the board of directors of their own companies (capitalist with a sprinkle of socialist).
By all his feats, Obama is a neoliberal (just like the majority of the USA Democratic party), a ideology that is well established to be a right-wing ideology. Yet right-wingers love to say that he is leftist. That is a form of propaganda used to shift the axis further to the right, after all, if you call Obama a leftist, then the "center" will be somewhere between the right and the right, and consequently even the most mild, obvious, and coherent leftist idea will be considered an extremist absurd.