Purpose of negative bias reference generator
You are right. The negative bias is there to add some tolerance to the situation when the input touches the 0V rail, so that this input voltage is properly handled by the circuit.

Even if the op-amp is rail to rail, if the op-amp's return is referenced to 0V, then an input that touches 0 is stressing that op-amp's maximum limit. The transistors in the output stage may switch from the active region to saturation.

If 0V is a value that is expected to occur as part of normal operation, it should be within the limit, not at the limit. A device should not be on the verge of breaking when presented with a valid, expected input signal.

So, the purpose of this LM7705 is to allow rail-to-rail amplifiers operated on single-voltage supplies to cleanly touch the lower power rail voltage.