A million years ago, when I first came to Japan, an American guy, who at that time had been here decades, told me that, "In Japanese, there is no concept of communication separate from the people involved." I think he was overstating the idea, but coming from an English speaking perspective, it does shed light on the issue you're talking about.
In English, we can say, "I've never had a fish as delicious as that!" Taken in complete isolation from any other context, this sentence contains no concept of the type of dialogue where it might be taking place. The word "that" does not contain that information. And, in English, we don't really care. It's all about the fish.
However, in Japanese, it's not cool to just leave out an assumption of who the speaker and audience are. You have to have some model when speaking of the kind of dialogue that is taking place. When speaking of the "deliciousness" of the fish, even though it's an ethereal aspect of the fish, it's still in relation to people. Maybe it's bound to an physical fish, or to someone's opinion of a fish, but the concept nonetheless will always have a position relative to two entities that are communicating about it.
So, I think the issue you're having is trying to see how 「こ・そ・あ」words point to things, without considering where they're pointing from. You're asking which of the three forms applies to a particular target, like the taste of a fish, but there is no one form like there is in English. In Japanese, maybe always, whether it's known, proposed, assumed, guessed, or however else you get there, you have to have a conceptual model of both sides of the communication taking place.
(In addressing concerns in the comments, I'm going to take a rather avant-garde route to explaining what I'm talking about, and I am up front about the fact that I am using the attempt to answer this question as a way of helping boost my own understanding, so if someone thinks this is wrong in some way, please do be constructive in your criticism.)
Image you're an author writing a book. You write a scene where your main character, Betty Hughenot, enters a room where all the guests of a party are gathered and having a lively discussion. Just as she enters, the last sentence that happens to be spoken is Joshua McDougal exclaiming, "... I've never had a fish as delicious as that!" As soon as Betty enters, though, the crowd turns to greet her, forgetting about Joshua, because she is a renown wit and everyone wants to hear what she's going to talk about. The story continues on, Joshua's remark is never referenced again, it was just something he happened to be saying when Betty opened the door.
Now, your book goes on to be a huge success, and it will be translated into many languages, including Japanese. When the Japanese translator has to translate Joshua McDougal's line of dialogue, she will go with:
{こんな、そんな、あんな}に美味しい魚は食べたことがない！
This is the ambiguity I think you're talking about. While Tim's very informative answer is correct about some factors that help you select こんな, そんな, or あんな, the choice is always predicated on knowing enough about the overall context that the choice is pretty much decided for you. However, in this case, we don't have that extra context to work with.
The translator must select one, but which one? The determining factors that would ordinarily tell us which to choose have happened before Betty entered the room, and are outside of the narrative. Maybe Joshua McDougal had just taken a bite of a fish present in the room, in which case こんな would work. Maybe someone else in the room just finished eating a fish and was crying because it was so good, and Joshua, seeing that person's expression, remarked on it, thus そんな would be right. Or, maybe in the room there is a painting on the wall depicting a fish being handed down to a chef from an angel descended from heaven, and, looking at the painting and commenting on it wryly, あんな could fit.
My point is just that you, as an author in English, didn't have to wrangle with an exact decision on how it is that Joshua came to be saying that when Betty entered the room, because in English, "as that" stands alone as being a universal designation pointing at the deliciousness of the fish. Some fish, somewhere.
A translator almost certainly would avoid the problem altogether with an entirely different sentence structure. But, in keeping with the spirit of the question, let's assume the Japanese translator has to use one of the あ・そ・こ words, like the sentence you provide. In doing so, that translator has to choose some model of where delineations are of in-group, out-group, and external to both, for the context of the sentence.
Let's say that the translator asks her publisher boss to contact the author about what exactly Joshua meant, but you've never thought about it that much, because your story is about Betty, and that statement was just filler. So, you say it's okay for the translator to pick whichever one she likes. The translator rolls a dice and goes with そんな. Now, every Japanese person reading that translated book will think that Betty walked in on Joshua observing someone else eating fish, or something like that. An impression people didn't necessarily get with the English book.
It's a subtle, but extant, difference. In Japanese, everything(?) is assumed to have some relationship to a speaker and a listener, and that is built into the language.
I hope that helps make clear what I mean, and if someone thinks I've got some part of this wrong, please do join in the discussion, I just ask that you do so in the spirit of helping educate, not merely disagreement. Thanks!
