Yes, theories and laws get proven wrong... because people were wrong about them, not because their fundamental nature changed.
Hedge mages ALONE make Thedosian magic unscientific.... it says clearly that they produce unique effects.
So, unless we're saying that some scientists can produce hyper-drives... while other scientists will produce warp gates... but neither group will be able to reproduce the other's findings... we're not talking about science at all.
It isn't a matter of incorrect classification... like Pluto isn't a planet anymore... "reality is change!" - nothing changed about Pluto at all. Science can change (because it's a make-believe system of classification) - nature never changes... and certainly not because you believe really hard.
Not all mages are born equally capable of the same thing... which is why you HAVE rote Circle spells... because those are grasped by the most mages... most of the time. Some mages can't even light little fires... "science" has nothing to do with it
Not all people are born equally capable of the same thing, if we were, we'd all be Einstein level geniuses, or better. Odd that you take that stand point about nature never changing, but then say that magic can't be measured or reproduced, since, on Thedas, magic is a natural phenomenon. Of course, a lot of this post is odd in the same way. You have narrowed to the field of science to what boils down to physics, but completely ignored things like Biology or Geology, or even Paleontology. All sciences, and none of them capable of building either device w/out detailed blue prints. The problem here isn't that magic can't be measured or reproduced, I've already shown that it can, the problem is that you are trying to quantify it with real world thinking, and it doesn't apply.
Regarding changes you discuss, what about gravity? For centuries Isaac Newton was the father of gravity, until Einstein proved him wrong. This isn't just a change in classification, but in how the entire system works, or seems to work. The nature of how it works never changed, what changed was our way of looking at what's going on. Magic is studied in the setting. We have people like Dagna to support that they can indeed dissect it, and get to the inner workings of it. If, as you postulate, it was all over the place random, you couldn't do that, other than to conclude that it's all over the place random. This isn't the case though, is it. We have specialist mages that prove you can focus your energies in one direction. We have jack of all trades mages, that dabble in this and that. The existence of these dabblers does not negate the existence of specialists. In fact, the existence of dabblers proves that some direction of will is required, and can affect what a mage "knows".
If there weren't specific "schools", they couldn't pick and choose. A hedge mage is simply an idiot savant. They have no idea what they're doing, and it shows in their results. However, if taken in to a Circle to be guided, they can learn to channel that energy. Yes, that means that they can be educated about their power, and how to more effectively use it. Teaching, training, it's all the same, it's all education. To use an example similar to yours, do you think a marine biologist could build a warp drive? Does their inability to build that warp drive mean that they aren't a scientist?