If a switching power supply has a problem with a modified sine input, then it is defective, whether it has active power factor correction or not. Still, it does happen.
Some loads, but hopefully not any switching power supply, will perform poorly with a modified sine source.
Pure sine wave inverters like those found in double conversion or online uninterruptible power supplies allow the output to be phase locked to the AC line so switching between the inverter and AC line can occur at any time without any discontinuity.