On the basis of numerical simulations, we explain the formation of the stable bound soliton pairs that were experimentally reported in a high-power mode-locked ytterbium fiber laser [Opt. Express 14, 6075 (2006)], in a regime where wave-breaking-free operation is expected. A fully vectorial model allows one to rigorously reproduce the nonmonotonic nature for the nonlinear polarization effect that generally limits the power scalability of a single-pulse self-similar regime. Simulations show that a self-similar regime is not fully obtained, although positive linear chirps and parabolic spectra are always reported. As a consequence, nonvanishing pulse tails allow distant stable binding of highly-chirped pulses.