> If the input current characteristics are outside allowable tolerances
This is the key to this whole discussion. I guess it boils down to existing line-interactive designs, why they can't work with simulated sine as a source.
A transfer-switch based UPS still needs to protect against brownouts, so it too has line behavior parameters outside of which it will switch to battery. It's an interesting question if/why a modified sine wave input would trigger that or not. Probably one of those "it depends on the design" things. (modified sine -> approximately an oscillating square wave.)
A dual-conversion (online) UPS is almost certainly more robust as far as what kinds of inputs it can accept (though as GP noted, they're more expensive, and they're also less efficient due to the additional rectification->inverter).
This is the key to this whole discussion. I guess it boils down to existing line-interactive designs, why they can't work with simulated sine as a source.