Another word that comes into play in this discussion is the word "proof". You can "prove" things in mathematics because no measurements are involved. In the legal system, "proof" is established by convincing a jury of one side or another of the legal argument, and having them render a judgment. In science, "proof" comes about pragmatically, through a preponderance of measurements and observational evidence that becomes so overwhelming as to be, in a practical sense, undeniable. Heisenberg's* Uncertainty Principle basically says that you can't "prove", in the sense of mathematical proof, anything that involves physical measurement.
That does not mean you can't establish an overwhelming degree of confidence in a theory, which allows the science to proceed forward. Scientists everywhere (real scientists, that is) understand this completely, and can also provide statistical evaluation of the degree of uncertainty in any set of measurements. Aberrational anecdotal incidents do not affect the data set, when the data set is stochastically large enough.
A good example of a thoroughly-established theory is the expansion of the universe, leading back to a conclusion we call, rather unfortunately, the Big Bang Theory. No reputable astronomer/cosmologist denies that idea anymore; the evidence for it is just too overwhelming. But even into the 1950s, there was a competing theory, the Steady State Theory, supported by numerous reputable scientists, including famously British astronomer Fred Hoyle, also the author of some well-known SF classics. Hoyle detested the idea of the "Big Bang" to the end of his life. He was wrong.
Einstein detested the theory of Quantum Mechanics to the end of his life, as well, and was likewise wrong.
I believe it was famous paleontologist/biologist Stephen Jay Gould who said, paraphrased: "The theory of evolution is supported by evidence about as well as any scientific theory can be."
There are good theories, supported by lots of evidence, and bad theories, supported by little, if any. To denigrate something in science as "just a theory" is an idiotic statement, and an egregious misuse of the word.
caw
*No, I am not referring to Walter White.