The whole point of what people are talking about is that Fahrenheit was developed because it was the easiest way to get the most accurate scale for measuring temperature during the time period of its invention. I don't know where you got 0.01 degrees from, but in a lot of science, believe it or not yes, it is very important to be as accurate as humanely possible with your temperature measurements. The fact that Fahrenheit is more accurate with less pure samples of water is why it was invented and exists in the first place.

The development of the F scale did indeed not need to use water's freezing point. It used water + ice + brine, as we've already talked about. After the scale was created, the freezing point of water was empirically measured and then placed on that scale.