In a previous paper [Phys.Rev.D82, 085016(2010)] we introduced a method for obtaining the exact Feynman propagator of a relativistic particle (for both Klein-Gordon and Dirac case) from a superstatistical average over non-relativistic single-particle paths. We suggested that this method could offer new insights into the currently much debated issue of emergent relativity. In this paper we proceed further, showing that a Brownian motion on a short scale originates a relativistic motion on scales larger than particle's Compton wavelength. Viewed in this way, special relativity is not a primitive concept, but rather it statistically emerges when a coarse graining average over distances of order, or longer than the Compton wavelength is taken. We also present the modifications necessary to accommodate in our scheme the doubly special relativistic dynamics. In this way, an unsuspected, common statistical origin of the two frameworks is brought to light. Salient issues such as generalized canonical commutation relations, connection with Feynman chessboard model, and Hausforff dimensions of corresponding path-integral trajectories are also discussed.