How can mixing flour with fruit juice be permitted on Passover, since all fruit juice, even pure juice directly squeezed from fruit always contains water?. Water, H2O, is simply a chemical component of fruit juice, as it is also of wine, milk and honey. Only oil could possibly be water-free. In substances like milk and wine there is always a large amount of water. This water is not added in any way, but part of the very definition of these substances. So to my knowledge such a mixture would be chametz.
There has become a shift in how people view chametz. In the times of the Talmud people talked about the physical signs of chametz, the dough getting cracks, turning white, or making a sound if you slapped it (it it didn't make a sound it was referred to as deaf dough). So it used to be that people would look at dough to tell if it was chametz, rather than rely on other things (like time) to determine whether or not something was chametz. The only scenarios where Chazal would use time to determine chametz would be in the instances where dough had been left unattended for a while. Which is why Rambam ruled that as long as you work the dough, it will never become chametz, no matter how long ago you added water to the dough.
Rambam's Mishneh Torah - Chametz U'Matzah - Chapter Five, Halacha 13
As long as a person is busy with the dough, even for the entire day, it will not become chametz. If he lifts up his hand and allows the dough to rest so that [it rises to the extent that] a noise will resound when a person claps it with his hand, it has already become chametz and must be burned immediately. If a noise does not resound and the dough has lain at rest for the time it takes a man to walk a mil, it has become chametz and must be burned immediately.
Then perception of chametz started to shift in a different direction. Rather than look for signs of chimutz, we started to worry about chametz before any visible signs appeared. And so by the time the Shulchan Arukh gets written, one could have invalid matzah even if no visible signs were present. According to Karo, if one worked the dough (and thereby warmed it with his hands), and let it sit for a few moments rather than rolling it out and putting it in the oven, it was chametz even if it had no visible signs.
Shulchan Arukh Siman 459:2
The dough should not be left idle for even a moment. As long as it is being used, even the whole day, it will not rise. If it is left idle for the time that it takes to walk a mil, it is hametz. A mil is a quarter of an hour plus a twentieth of an hour. After dealing with the dough and warming it with your hands, if it is left idle, it will rise immediately.
And now we get to the modern time where people think that any contact with water automatically makes something chametz, causing people to erroneously think that water is what causes something to become chametz, but this is not true. In fact this idea is so foreign that Rambam wouldn't even understand what you are talking about, as this ruling of his will illustrate.
Rambam’s Mishneh Torah: Chametz U’Matzah Chapter 4 Halacha 10
Grain upon which [water] leaking [from the roof] has fallen: As long as [the leak] continues, drop after drop, it will not become chametz even if [the leak continues] the entire day. However, if [the leak] stops, if it remains [untouched] for the standard measure [of time] - behold, it becomes chametz.
So the reason that juice doesn't ferment probably has nothing to do with water content, as water doesn't automatically make something chametz. For even continuous dripping of water is enough to prevent grain from becoming chametz.
So what is chametz? Chametz is the process in which the yeast that is floating in the air around us, lands in dough we are making, and if the dough is wet and is not worked (because yeast needs a calm environment in order to thrive), the yeast is able to reproduce and eat, producing gasses which make the dough rise. Therefore what makes something chametz is whether the mixture of liquid to grain/flour is hospitable for yeast to grow and propagate. i am not aware of any reasons the Rabbis give for why fruit juice (or milk for that matter) stops bread from becoming chametz, i can only turn to science to find answers. So while there may be water in fruit juice, maybe there isn't enough water in the juice for the yeast to ferment, or maybe there is too much sugar from the juice and the yeast can't handle it, thereby preventing any chametz. Water isn't the issue, it's the yeast that floats in the air all around us that lands in your dough while you are kneading that is the issue.
So what likely happened was that the Rabbis of the Talmud, and thereby the Rambam, and even Karo had probably noticed that when you mix fruit juice with flour, the dough never takes any signs of chametz. And since it never shows any visible signs of become chametz, then clearly it's not chametz, despite the fact that water exists in fruit juices. If you have any doubts of this, mix fruit juice and dough and see if it ever rises, and you will have the answer to your question.
The laws of mixing fruit juices with flour derive from two seemingly irreconcilable Talmudic teachings:
אמר רבה בר בר חנה אמר ריש לקיש: עיסה שנילושה ביין ושמן ודבש - אין חייבין על חימוצה כרת
Rabba bar bar Hanna said in the name of Reish Lakish: Dough kneaded with wine, oil or honey that rises is not forbidden as chametz (Pesachim 35a)
והתניא: אין לשין עיסה בפסח ביין ושמן ודבש. ואם לש, רבן גמליאל אומר: תשרף מיד, וחכמים אומרים: יאכל
It was taught: It is forbidden to knead dough on Pesach with wine, oil or honey. If someone did knead such a dough — Rabban Gamaliel says it must be destroyed immediatey. But the sages say it may be eaten. (Pesachim 36a)
Although the initial statement implies that only water causes the kind of leavening the Torah deems as chametz, various interpretations on this teaching have led to various traditions. The Ashkenazic custom to generally refrain from dough kneaded with fruit juice during Passover is derived from Rashi's understanding (Pesachim 36a) that such a mixture, while not full-fledged chametz, was nonetheless forbidden by the sages for being chametz nukshe - a lower category of almost-chametz.
However, many authorities, starting with Tosafot, have contested this interpretation of the Talmud, insisting that pure fruit juices alone cannot make chametz; the second Talmudic passage here means that it is forbidden for someone to add such liquids into a dough already containing flour and water.
Sephardim follow the ruling of the Shulchan Arukh (462:1), which allows fruit-based dough, based on Tosafot's understanding of chametz.
Even though H2O exists in fruit juice, the lenient opinions understand pure water as what causes the Torah's definition of chametz. If you're looking for a finer distinction, see R. Ovadia Yosef's responsum (Yabia Omer 9:42), in which he asserts that rising agents added to Pesach cookies made with fruit juice help makes the dough puff up, but do not technically leaven the dough. In his understanding, even when other ingredients make a dough appear to be chametz, it is only when grain is moistened by pure water that a product can be considered chametz.