Dinner, I'll reply later.
Synopsis: Since divine revelation is claimed, it would (if true) trump other considerations. The canonical objections to this are (as you noted in an earlier post) "how do I know WHICH God" of "anyone can claim a "god", how can you tell the difference". These both arise from the inability of the scientific method to differentiate between unfalsifiable claims; and the Flying Spaghetti Monster is a wonderful satirical illustration of the principle. The answer to this is that there are portions of human experience which for one reason or another are not susceptible of examination by emprical, falsifying methodologies. To distinguish between them, other, more subjective methods must be used. Note by the way that although empiricism, through the means of falsification, provides a way to whittle down errors, this does not necessarily mean that other forms of acquiring knowledge MUST yield incorrect results; but it does mean that they are more liable to do so, having no "internal" correction mechanism. Look at my oft-quoted chestnut about the Physics Today article where the lawyer won a car-crash lawsuit by saying "...everyone knows the laws of physics are obeyed in the laboratory, but not in rural New Jersey." This lawyer and the conclusion of the jury were incorrect; but it does not follow that ALL jury decisions are incorrect. It's just that when you use scientific, empirical methods you can "tell for SURE" that something is wrong.
Which brings us back to your question about a jury trial:
In the case of a criminal jury trial, the rules are that the defendant must be presumed innocent, until proven guilty "beyond a reasonable doubt."
Call that placemarker 1.
Think of the vernacular, the common parlance, say in a sporting event "a miracle comeback". We know that Miracle Comebacks happen--look at the #&#@!! 1969 Mets beating my beloved Orioles in the World Series, or the 1980 US Olympic Hockey team kicking Soviet ass.
By that definition, "miracles" happen--they earn the sobriquet "miracle" because they are rare.
Call that placemarker 2.
In a jury case, "reasonable" doubt is rather a nebulous phrase...Some things may actually happen, but they happen rarely enough that one discounts their occurrence with "other things being equal". ECREE and all that.
Call that placemarker 3.
But a jury trial (saying whether something is LIKELY to have happened) is not the same thing as science and/or empiricism, where you are trying to come up with a concise self consistent model of what "did" happen (subject to revision according to new experimental evidence).
Here, the miraculous refers not to what is "likely" or "common" or "reasonable", but introduces in addition the element of extra-natural, "super"-natural entities. This complicates matters in several aspects.
1) First, since "by definition" (so to speak), the supernatural is "super" natural, it is by its essence not subject to the type of tests, verification, and refinement the way a construct within a model may be tested. Think of this as "how many angels CAN dance on the head of a pin" ? It's harder to come up with a consensus answer which can be falsified or verified by experiement when you can't even agree on what signal is unambiguously that of an angel :-)
2) Second, since (by common agreement, reputation, what have you) the supernatural entities are "sentinent" (whatever THAT means!), you don't know for sure whether they are playing fair, or whether they are subject to uniform rules of behaviour on an individual instance-by-instance basis. There is some analogy here to psychology as "cargo cult science". Or to the line on the Murphy's Law poster that "under the most rigorously controlled conditions of humidity, temperature, and pressure, the organism will do as it damn well pleases!" :-)
3) Third, the concept of the supernatural, and its impingement (infringement?) upon the orderly, predictable, natural world, works against the entire ansatz of the empirical method -- "uniformity of causes in a closed system". And more's the pity, it violates BOTH of the tenets at the same time: and inconsistently. First the supernatural opens up the system: and if the supernatural agent under consideration has any choice in the matter, it can either interfere or forbear, without prior notice, in any given situation. So you don't even get a useful fudge factor or cosmological constant out of it. :-(
4) Finally, the three points above would completely RUIN the supernatural as any form of efficacious MODEL or reason, rationale, cause of things. (*)
But there's the rub. I don't happen to think that Judaism/Christianity came about, or were designed, as an attempt to "explain" a confusing world. The language and the stories related in the Old Testament are primarily talking about how God is concerned with human behaviour, rather than "why does water freeze when it gets cold" or "why are their seasons?"
(*) BTW, there is a confusion of language: "because" can refer to "cause and effect" (he got wet because it was raining) , or it can refer to a "motivation" or "grounds" (he got wet because he forgot his umbrella). There is some analogy here to the French savoir vs. connaître. Science is based on observation of phenomena under controlled conditions, and deals with specific fact knowledge. Religion is based upon experience, authority, or revelation, and deals with "acquaintance" knowledge. Religion is not INTENDED (so to speak) to address the types of questions asked by science. In other words, it is not based upon EVIDENCE; but upon TRUST. And we all know there are such things as charlatans; but that does not mean that anyone who trusts is necessarily incorrect.
Finally, one last point about jury trials: miracles are commonly assumed to be at the behest of God or Angels (The Good Guys). Part of the credulity about an accused criminal getting off by a miracle is that the net effect of the miracle would be to harm someone (the victim) or to enable a bad guy (the criminal) to prosper. Both of these activities are antithetical to how God is "supposed to" act, in the common everyday view of things.
Cheers!