I'm interested by your choice in example, because it seems contradictory to your claim. To continue your example, if a judgement is "more true" then other judgements, it would also be correct to say that it is the "least false" of the other judgements. By its nature, then, it qualifies for both prepositions: it can lay a claim to be both A) true, and B) false. While the concept of true and false is mutually exclusive on paper, in practice the norm is for some form of equilibrium to be met between the two conditions. "More true", as you say.
Think of it like this. Ideas are a compliation of many things. They have reasons behind them, causes, different expressions, and variations. Each idea is composed of hundreds or thousands of "true/false" things. These are evaluated individually, and then quantified later to arrive at whether something is "more true" or "better."
For example with food, you're not looking at one aspect. You're looking at taste of individual parts, texture, appearance, flavor, temperature, proportions, preparation, serving, finesse, and many other things. Each of these you can break down to a statement of what is 'better' than another.
So for let's say a hamburger, we have the meat. You arrive at the conclusion it's better than another. Why is that? Different people have different tastes, who are you to say it's better? Well, you're looking at it in an objective way (hopefully) and evaluating everything, even if it's not consciously. At some point, you found how cooked it was arguably better. But why? That's still an opinion, isn't it? So then we look at what it actually is. Are there any raw spots? Y/N. Is it still tender? Y/N. Does it still retain the juices? Y/N.
Taking that further, you can break down to why raw spots are 'better' or worse than fully cooked, by going into fact. Raw spots mean there might be bacteria still, so even if you like raw food, it's not 'better' than cooked food.
I could go on like this for a while, because there's really no end to it. Each component is made up of parts which is made up of different areas which are evaluated based on certain criteria because of arguable FACT. There IS a true/false in everything, there just can be quite a few, and in different places.