You misunderstand. The burden of proof is on the one making the claim, which is you.
No, you are the one misunderstanding. If so-called "homophobic" people make the proposition that homosexuality has no biological cause, and others reject that proposition and assert homosexuality is biologically (and that includes genetically caused) then it is up to those in science to disprove the proposition that homosexuality is not biologically caused.
They need to come up with a hypothesis explaining this phenomenon and test it out. And then either reject or accept their hypothesis.
That's an example. So, you'll seek to find a "gay gene" or "gay genes" or some other biological cause. Or you'll more accurately propose there is no statistical link between "gene x" and "outcome" or "trait y," and when finding a statistical link you'll reject your hypothesis, or in this way disprove your hypothesis.
If you are asserting there is a natural explanation for case in which a spontaneous cure happens for an individual, in which medical science, the medical professionals have already stated that there is no natural explanation, then the burden is for you to disprove those medical professionals offering their professional opinions from the
applied science of practicing medicine. And the practice of medicine is an applied science like engineering. You seem to be confusing it with primitive medicine men who used plants, prayers, and drawing on bodies to produce cures.
If we have no way of knowing, then how do we know that it is even supernatural? Again, this is just an argument from ignorance.
Supernatural is a concept. Meaning it is above and beyond the natural order of the world we live in. We can't observe ourselves from outside the natural world. In other words we can't stand outside the universe and observe the universe. So, we are in the dilemma that the scientific methods has its limitations.
Those that respect science while at the same time acknowledging the limitations of science
are not referred to as believers in scientism. On the other hand, those that believe science has no limitations in providing explanations, and that therefore science can eventually explain everything are referred to as believers in scientism.
We can refer to rare physical occurrences that defy the laws of chemistry and physics as miracles or the supernatural. Because they exhibit characteristics that go beyond the natural order of things. In that sense it is not necessary to have scientific evidence of a supernatural substance or supernatural substances. Until otherwise proven false we can apply a term that is descriptive of some phenomenon that occurs defying the natural order, and for reasons we can't scientifically explain.