The point about offices is that the root cause of the issue is the design of the space.
The point about white noise is that an open office should have about 45db of background noise (white or pink). This means that a person is less likely to hear a normal voiced conversation 20 feet away.
What makes noise distracting is that it stands out from the background (just as automotive headlights stand out more at night than during the day).
I'm not sure who came up with the "should have 45db of background noise", but I worked in an environment like that for years and never liked it. Others I worked with felt the same way, and some dismantled them. I don't like audible distractions, but I think reducing them is better than trying to cover them up with even more noise, unless you are sleeping. If you do use noise, I think natural running water or a fan is better than digital.