What my question is really trying to ask, is if it's possible that some alien race possesses technology far more advanced than our own, but also have an interpretation of physical results that is less experimentally accurate and less mathematically consistent?
To provide context, I'll give the story explanation for why this is the case. In my story, it is relevant to the plot that there is a galactic regime limited to strictly galactic or inter-stellar travel. They aren't capable of inter-galactic travel, because they are limited to propulsion that is only fast at the inter-stellar level. The reason for this and other limitations, is that their theories of physics can't account for the physics more advanced tech. This is due mostly to their alternative interpretations of quantum mechanics, gravity, and classical laws. The source of this difference, is that their scientific philosophy isn't concerned with how things really are, because this race only ever pursued science to the end of its' practical applications. They never really had a thirst for "knowledge for its' own sake". This got them quite far, but their interpretations lead to explanations that don't account for higher physics. For example, they don't have a theory of quantum gravity, because the problem doesn't exist; they don't have quantum field theory or general relativity, because they have a different explanation for experimental results.
The reason their solutions are not our own, yet theirs are both less correct but also more useful, is because they don't have our philosophy of science. They don't care about understanding reality's nature, they care about utility, and so they only measure scientific merit by the concrete, tangible ability to give new technologies, rather than our more abstract criteria. If the theory's physics allow for tech, and the tech works, then its' been validated. If a theory allows more tech, then that's the right one; That's all there is to it. Their interpretations work well enough to give them tech, so they don't question it. On the other hand, QFT, GR, etc, satisfy our more abstract criteria for correctness, but that's very different from a scientific method geared towards utility; Our theories may be more likely to be correct according to well-established philosophical criteria for empirical correctness (the scientific method we came up with), but this species measures by model utility, not model accuracy, and more accurate models are not necessarily more practically (read: "engineering-wise") useful models; Our theories are accepted because they are more accurate based on the criteria for empirical correctness, but while our theories do allow for new wonders of technology, they aren't exactly known for their ability to do so, which their scientific method is based on; This means they would logically dismiss our own ideas. Even if the theory is not as mathematically developed or experimentally accurate, simpler but less accurate models can be more useful in engineering than complicated explanations.
Because of this, they did not care about the explanation that best revealed the universe's nature, only what best revealed new technology, and so they never discovered the true ultimate theory. When they realized they couldn't escape the galaxy and couldn't do some other things, they began doing more physics work to reveal technology that would enable this. But, only the universe's nature would reveal such technology, and to find it, they had to solve for another problem; Historically, they had no care for pure mathematics (only applied math, due to their utilitarian views precluding any incentive), which meant that they didn't even have the mathematical concepts required for higher theories. As a result, despite being more advanced technologically, they actually have to catch up with us in the realm of the pure mathematics (i.e., they have no concept of lie-groups or fiber-bundles, and they aren't used to thinking so abstractly). And due to their regime, which is a hard-communism even worse than the soviet union, science doesn't really experience breakthroughs; Only cautious incremental steps. Also due to their regime, alternative knowledge often gets snuffed out, alternative tech rarely gets a chance to flourish, and every other race more advanced was also a predecessor that already went extinct, so their knowledge has been buried in history.
However, I'm not quite certain how to explain their ideas in a self-consistent way. So what I want to know, is if there is a case in physics where a theory couldn't be the real case, due to mathematical inconsistency or experimental inaccuracy, but from an engineering point of view the theory was not just more useful, but useful enough to allow technological advancements faster than the more accurate model? I'm also asking if this could be extended so dramatically, that you could get a situation where a theory allows things like warp-drives soon than a more accurate theory, but experimentally or mathematically isn't as close to truth.