Great question, Jochen. I always sticked to "magic is rare, only seems predictable for some, and has always a flipside".
Magic is rare
Although D&D is a setting with high fantasy elements and thus with a lot of common magic, magic is still rare, meaning that high magic is not something common, even in D&D. On the other hand, you can purchase magical items in shops, spells and potions for almost everything, magic is known to a crude degree to the common people, and there are a lot of magic users.
Let's speak rough percentages. How likely would be a wizard in a small village? Very unlikely. In a town? More likely. And in a city. Very likely. I would assume that there are even several wizards in the capital. Wizards flock to locations of learning. So what would they do in a village? Nothing. Oh, they may be able to help, but they are from a different world. And all their fancy Aethermancy and dimensional studies, demonology or even their power over fire will seem useless for villagers who need good weather, a cow that gives milk and a healthy baby. And they on the other hand might die from boredom. Likewise, I would not assume that there were many magic items in a village. Of course, this could be a quest if something like this happens in a village. An event the locals will talk about for generations. So coming back to your own example, here in a small village, if you did something wrong, you will be dealt with directly and without the use of magic, or you will be accompanied to the next town (which is more trouble for the peasants).
And the more cultivated and learned the background gets, the more is it likely to happen upon magical means used by the locals. There could very well be a wizard in town. But with all the different ways of magic, how likely is it that (a) there is a wizard, (b) that he is not busy with other things, but free to help and (c) willing, and (d) takes on an official title in town? Again, how much less likely is it, that he (e) actually knows these kinds of spells? A true truthsayer in a city might be in comparison very rare! The more magic variety there is and the more restricted magic becomes due to powerful magic in the world, the less likely it is that magic mingles with the commoners' lifes. At least, that's what I believe.
And then again, where there are forces of magic and good, there are always those that stand against them, want their power, strife to push them out of their "unfair" office, try to force their will unto them or pay them off for their own agendas.
I personally find it fantastic to introduce a truthsayer to a court, but not on regular basis. Last month's truthsayer may have found a sudden visit by a relative of the condemned to be more than what he/she could handle. Some may be well protected and stay in office long. But then, these towns will probably be renowned for them and hard judicial cases will be brought forth to them to be dealt with, like they would be brought to a temple of a truth saying diety. And even magical items of the sort are hard to keep save when there are contradicting agendas, jealousy between cities and guilds, or even the danger magic bears itself.
Magic only seems predictable
Magic is like physics. We know a lot about the world thrue the eyes of physics, but there is even more that we still don't know. Likewise, even if the standard wizard is sure about his magic formulas, I like to sprinkle wonder and excitement back into this magic-science approach by sometimes letting things happen that are unpredictable (and a new quest or mistery).
Magic has a flipside
Magic has a price, can be used against the user, has forces behind it that many do not understand. Using this "rule of magic" for example, there could indeed be a magical artifact for truthseeing in a town, but the townsfolk have either learned to fear the use of it because it could result in chicken-plagues, or they have accustomed to and relied upon that item so much that they won't believe anything someone says without such proof. Maybe the artifact is set to too high degree resulting in every uneasiness of the victim to be a blatant lie resulting in death. Or all the people suddenly want the artifact for themselves to make sure that no one is lying to them ever again. Again, nice as quests.
That said, I think you CAN change and reinvent the setting by taking into account the influence magic of a system would have on it, but I would usually refrain from overdoing it. The players have specific expectations and wouldn't follow your 2-3-4 steps of ensuring truth and what powers there actually are in the system which could be used and which the PCs should have known. If you want to do this, you should directly talk with the players about it and introduce it gradually.
(My players were once shocked when I showed them how easy it would be for the corporate investigators in Shadowrun with all their technological and magical advancements to identify the culprits of a deed, i.e. their PCs. And they still didn't even get half of what I researched about what possibilities there were.)
