But you didn't, you supported a connection between mind in brain, which ALL mind-body philosophies accept for the most part. Here's a comparative illustration:
A creationist tells you creationism is true based on the evidence that there are gaps in the fossil records. You explain that gaps are to be expected even without creationism due to how fossilization occurs and that this isn't actually evidence of creationism. They then switch the burden to you and ask you if you have evidence to the contrary. Not only are you under no obligation to provide evidence because of the shifted burden, but even if you COULDNT this would not make creationism true by default.
Now switch creationism with materialism and you should understand where we are.
Except the burden is still on you to support your claim that the mind is
independent of the physical brain. The assertion the mind IS dependent on a physical brain is supported by all the observations we make about how the brain works - a physical alteration to the brain can result in alterations to the mind.
To use your analogy, imagine a creationist claiming that all life is created, and a non-creationist pointing out all the evidence that life shares common ancestry and asking for evidence that life was created. Rather than providing evidence for creation, the creationist simply asserts that just because the evidence demonstrates common ancestry, it doesn't
rule out creationism. But the point isn't that one set of evidence necessarily
rules out the opposing proposition, it's that
there is evidence for only one of two given propositions, so the assertion of one is erroneous and can be dismissed as having no rational basis.
That is exactly what you have just done.