With the resistors connected to the inverting input, the op amp looks like an open circuit for output voltages below the threshold (where the diodes don't conduct).
Thus its resistor is effectively removed from the circuit. Once V_out crosses V_th, the op amp holds its end of the resistor at V_th, just like throwing a switch. That results in a gain change in the voltage divider, but ideally no voltage step.
It's a similar idea to the two-op-amp absolute value circuit, e.g. Fig
4.46 of AoE II. (iirc you don't have AoE III.)Cheers
Phil Hobbs