An unprejudiced analysis is made of the possibility of different theoretical descriptions of the decays phi --> rho-pi --> pi+pi-pi-0 and phi --> pi-gamma, taking into account both the phi-omega-mixing and the direct decays phi --> rho-pi and phi --> pi-gamma. For this purpose the data from the Neutral Detector on the reactions e+e- --> pi+pi-pi-0, pi-gamma, K(L)K(S) in the interval square-root s = 700-1050 MeV are used. Experimental data are shown not to permit one to answer the question: What is the origin of the decay phi --> rho-pi (pi-gamma)? This decay can be almost completely caused either by the phi-omega-mixing or by the direct decay phi --> rho-pi (phi --> pi-gamma). Intermediate cases are certainly possible. It is shown that to elucidate the situation at least an order of magnitude improvement of accuracy is required. Possibilities of studying this problem on the collider VEPP-2M and phi-factories are discussed.