Thank you for putting the effort into boiling down your exact problem in interpreting Dick's results. I think that will help resolve the problem.
I think you are confusing Dick's "model" with the "pipeline". In the pipeline analogy, let's say information flow is from left to right. At the extreme left is ultimate reality. At the extreme right, just beyond the spigot, is our conscious human awareness with its logico-deductive capabilities. The only information we (meaning our conscious, logical, analytical selves) have available to us is what comes out of the spigot. That means we don't even know if there is a pipeline, and if there is such a thing, we certainly don't know anything about what goes on inside of it. What we are trying to figure out is the nature of ultimate reality, i.e. the ultimately original source of the information coming out of the spigot.
Now, what does it mean to "figure out the nature of ultimate reality"? Well, it means being able to communicate that nature to another conscious, aware person. How do we achieve that? We do it by building a model which is a vast simplification of the thing we are trying to communicate, but which reflects in an analogous way, the things or aspects that we claim to have figured out.
For example, you know how a car engine works. Just think about how you would explain that to a six year old kid. You would construct a model, either in words, pictures, or maybe even using things like tin cans and coat-hanger wire. The point is that you would greatly simplify the real complexity of a real engine and present a model that has the essential features and functions of the real engine. The model needs only be sufficient to turn on the spark of understanding in the 6-year-old, so that when he/she says, "Oh, I get it", you can stop. And even though your model might have been perfectly suited for the 6-year-old, it would be laughed out of a college class in IC Engine design. There, they would use a more sophisticated model, but a model nonetheless.
Now, as far as ultimate reality is concerned, we each find ourselves in posession of a mental model of reality. We don't really know how we got it, and we frequently find that it is wrong in certain ways. We notice that we continually adjust that model as we learn more by living.
Typically, at any time in history, there is sort of a concensus of the models held by people of the time, and just as each individual's model gets updated over time, so does this concensus model. In the past two centuries, science has taken over the position of being the authority on which current concensus model is the most nearly correct. And, I think that is a vast improvement over the times in which various religious organizations have held that position.
But in all cases, the concensus model was arrived at by starting with people's mental models and testing them against the information coming out of the spigot and refining the models to be able to figure out what must lie clear to the left of the pipeline, as I described above. That is what Science does.
Dick asked the question, can we know anything about that ultimate reality without starting from any existing model and without assuming anything about any pipeline or what might go on in any pipeline. That is, all we have to start with is that something exists clear out there to the left which is the ultimate source of the information coming out of the spigot. Since we are attempting to figure out something about it, we assume that we will be able to describe it in some sort of model as I have described.
So Dick starts with this blank model, which is going to end up being the explanation of ultimate reality he is going to give to a 6-year-old kid, or a college class, or whomever, and begins to construct it using pure logic. In anticipation that there will be considerable, unpredictable and unknown distortion of the information about ultimate reality as it flows through the pipeline and before it comes out the spigot, his model, which you could think of as a bucket under the spigot, has to be able to reflect any possible such distortion.
So if, for example, the pipeline introduces some kind of symmetry, the model must be able to reflect that symmetry. That is specifically in order to reflect what might go on in the pipeline and has nothing to do with the original input to the pipeline. The only assumption on that original information is that it is possible to communicate some features or aspects of it in language, or numbers.
So to sum up, when Dick says his "bare model" must display every symmetry he can think of, he is talking about the bucket and that it must be able to display any symmetry that the pipeline might have introduced to the information.
That way, his "model will not attribute to reality things which could have been generated by the pipeline". In other words, if, by chance, the pipeline did introduce symmetries into the data we see, Dick's model will accommodate the symmetries without assuming they came from, or were inherent in, the ultimate reality itself.
Or, in Dick's words: "By this mechanism I assure myself that my model will not attribute to reality things which could have been generated by the pipeline."
I hope this helps.