Low-cost solution-based synthesis of metal halide perovskites (MHPs) invariably introduces defects in the system, which could form Shockley-Read-Hall (SRH) electron-hole recombination centers detrimental to solar conversion efficiency. Here, we investigate the nonradiative recombination processes due to native point defects in methylammonium lead halide (MAPbI3) perovskites using ab initio nonadiabatic molecular dynamics within surface-hopping framework. Regardless of whether the defects introduce a shallow or deep band state, we find that charge recombination in MAPbI3 is not enhanced, contrary to predictions from SRH theory. We demonstrate that this strong tolerance against defects, and hence the breakdown of SRH, arises because the photogenerated carriers are only coupled with low-frequency phonons and electron and hole states overlap weakly. Both factors appreciably decrease the nonadiabatic coupling. We argue that the soft nature of the inorganic lattice with small bulk modulus is key for defect tolerance, and hence, the findings are general to other MHPs.