YEs, alcohol and water mix, but when they did, they no longer mix with the gasoline.
Try a little home experiment: mix some alcohol and gasoline together in a glass container (so you can see what's happening): shake it up and they mix completely - gasoline and alcohol are miscible.
Then add a little water and shake again: the water mixes wtih the alcohol and separates from the gas completely, so if your vehicle is jetted or calibrated for the gas/alcohol mixture, it is NOT going to run the same.
...but it will run much better than a gasoline engine would on the same amount of water injected into its fuel .
In the work cited, Mr. Matheson addresses this:
Alcohol blends do have one relatively minor drawback. The presence of even small amounts of water in the blend will cause a portion of the alcohol and gasoline to separate. At room temperature, less than 1% water can do the damage. As the temperature is lowered, amounts as small as 0.01% can cause separation. However, various substances such as benzene (benzol), acetone, and butyl alcohol can be added to the blend to increase water tolerance. Closed fuel systems, now in use, prevent moisture from forming inside the gas tank. Oil companies, given the proper incentive, could dry out their storage facilities and pipelines. Also, extensive use of alcohol blends over the past 50 years is ample evidence that the problem can be solved.
There are additives, non alcoholic, which can be added to fuel to allow a small amount of water to blend. I have been told many times over the years that adding alcohol to fuel may increase rust problems. In a couple of cases in years past I've added alcohol to the gas tank to remove a large amount of water. Probably didn't cause it to mix with with the gasoline but allowed it to burn in order to keep the engine running. I wouldn't do that with the modern fuel injected cars. The carburetor was more tolerant of a little water for a short period of time.
Actually, isopropyl alcohol (rubbing alcohol, fuel-line anti-freeze) is great at mixing with both fuel and water at the same time, which is why it is used as a fuel-line anti-freeze, among other reasons. Ethanol and methanol aren't as effective for co-miscability.