Before revision:  If the protein explores the native-like states for a time much longer than the time to overcome the free energy barrier,  the resulting FPT distribution may be approximately single-exponential, as is expected for two-state folders, but the mean FPT (MFPT) to reach the native state will be determined by the time to find the native state among the native-like ones.
After revision:  If the protein explores the native-like states for a time much longer than the time to overcome the free energy barrier, the resulting FPT distribution may be approximately single-exponential, as is expected for two-state folders, but the mean FPT (MFPT) is determined not by the height of the free energy barrier but by the time to explore native-like ones.