Yes, you are right, the closer to zero the better.
But another puzzling fact is that he adjusts the reference, which means will be higher. So if the intention is really to detect a voltage as close to zero as possible, why not leave the reference at its minimum, why adjust it higher, which will also increase the threshold?
Initially I thought he wanted to actually detect crossing through 2.5V or so, since the input is marked 0-5V. But why do that? If the input was really limited to that range, then you could just convert it directly using the ADC, no need to rectify it and detect the negative part.
Perhaps the author has found some peculiarity if the chip, so that with a negative input, but a certain positive reference, it somehow produces an outpu pulse. It's hard to believe, but it migh happen. After all, there is a buffer opamp inside. If it suffers from phase inversion, then it could do that.
If that is the case, then it's not a normal mode of operation, not one I would rely on for proper operation.