Without seeing the schematic of the circuit which are fed these signals, is difficult to speculate.
I have used the single diode precision rectifier when I want to detect precisely a zero voltage crossing with a comparator.
The ubiquitous LM393 has an input common mode range which includes -300mV, even with a single supply. Thus by feeding a signal that slightly goes below zero, you can be certain that the exact zero volts, plus or minus the small offset voltage, is detected.