Here's why it is considered the norm to use distilled over tap water- consitency.
Believe it or not it tool me a LONG time to find the answer on the intertetz. Everyone talks about the importance of calibrating with distilled, but almost no-where does it explain why.
Everybody's water is going to be different, everyone's plumbing is going to be different, we know from brewing that different regions have water with different mineral content- Like Burton on trent for instance. Even boiling different waters aren't going to make them all the same.
This would explain why the factory sends these out calibrated with distilled water, but not why
you would calibrate with distilled water. When you calibrate your device, you don't really care what the water is like in various parts of the world, but only with what your water is like today for your brew.
You basically want to zero out your test device, and you want to know it is zero, or whatever the calibration standard is. It's like check the accuracy of a scale in the old days with a standard weight set. You want to trust that a gram is really a gram, before you measure whatever is important to you.
To zero a scale, you don't need a standard weight set. Using a standard weight set to correct a scale would correspond to finding a correction factor for your refractometer when using it with wort as opposed to clear sugar water. Zeroing a scale would correspond to zeroing your refractometer.
From what I've heard, it doesn't sound like it makes much difference whether we use distilled or tap water. However, to the extent that it may make a difference, it certainly seems we should use the water with which we brew. Here's an analogy:
The scales we use to weigh our ingredients may arrive from the factory "zeroed." If so, they will calibrate zero by using no basket on top. The reason is for consistency. We all use different baskets to hold our ingredients together on the scale for weighing. However, I want my scale to read zero when
my empty basket is on it. An empty basket is weight on the scale, but it is not what we want to measure, so we treat it as if its weight is zero, so that we get the weight of our ingredients. When it comes to using a refractometer to measure the sugars we place in our water, we want to measure those only. The tap water or spring water is only the "basket" we use to hold our extract. Even your hydrometer may not read zero if you have a lot of mineral content in your water. To find our how much sugar you have dissolved in that same high mineral water, you'd want to zero your hydrometer (not normally possible except by subtraction) to the high mineral water not to distilled water.
A mathematical proof:
Specific gravity minus 1 is a linear function of the ingredients we put in our wort. The vertical intercept of that linear function is zero--the equation is of the form y = mx. If we put in 3 times as much extract, we expect 3 times the number of gravity points. As I understand it, Brix is not precisely a linear function, with vertical intercept zero, of specific gravity since the conversion formula is not as simple as y = mx. However, it is extremely close to such a linear function. So much so that that I can't detect the difference between a standard conversion table and the formula y = 4x (x=brix and y=(SG-1)*1000, of course) until I reach a level in the neighborhood of SG=1.080 and then it is so close it is hard to care about the difference. Furthermore, even at that level and beyond, 4x hits below the true conversion, so (4 + very little)x would be an even closer linear function. Thus, since the function between brix and gravity points is (almost precisely) linear with vertical intercept zero, and the function between gravity points and dissolved sugars is linear with vertical intercept zero, the composition of these two linear functions is (almost precisely) linear with with vertical intercept zero. Given that what we wish to measure is dissolved sugar (not mineral content), we should zero our refractometers with our brewing water rather than with distilled water.