You misunderstood what I have said.
All causations are inferred from correlations. But not all correlations are inferable as causation.
If observation of correlations is the only way to infer causation, then the evidence of people having, remembering and subsequently reporting complex, coherent experiences, logical thought processes, and veridical perceptions from an out-of-body perspective during clinical death or impaired brain functioning certainly thwarts the inference that consciousness is a product of brains.
Perhaps an even more definitive repudiation of the idea that brains produce consciousness are the correlations produced by the US government's own research on anomalous cognition,
as statistics professor Jessica Utts noted when asked to examine the findings:
Research on psychic functioning, conducted over a two decade period, is examined to determine whether or not the phenomenon has been scientifically established. A secondary question is whether or not it is useful for government purposes. The primary work examined in this report was government sponsored research conducted at Stanford Research Institute, later known as SRI International, and at Science Applications International Corporation, known as SAIC.
Using the standards applied to any other area of science, it is concluded that psychic functioning has been well established. The statistical results of the studies examined are far beyond what is expected by chance. Arguments that these results could be due to methodological flaws in the experiments are soundly refuted. Effects of similar magnitude to those found in government-sponsored research at SRI and SAIC have been replicated at a number of laboratories across the world. Such consistency cannot be readily explained by claims of flaws or fraud.
The magnitude of psychic functioning exhibited appears to be in the range between what social scientists call a small and medium effect. That means that it is reliable enough to be replicated in properly conducted experiments, with sufficient trials to achieve the long-run statistical results needed for replicability.
You can find no example of a causation where the evidence is not a correlation. Can you find any?
The cause of black holes was not inferred from observed correlations, but was deduced from the mathematics of General Relativity.
The various effects that are the result of the Higgs field were not inferred from observed correlations. Rather, a field was hypothesized to exist and exhibit characteristics that resolved certain observed anomalies (such as by giving mass to some fundamental particles). Perhaps one can say that the detection of the Higgs boson involved observation of correlations, but causation was not inferred from such correlations.
The cause of an incident of anesthetic awareness is not inferred from observed correlations. Under normal circumstances, there are 3 possible causes: the patient received an inadequate amount of anesthetic due to doctor error, equipment failure, or characteristics of the patient (e.g., tolerance to one or more of the drugs). The possible causes are eliminated until there is only one left.
To observe that thunder often follows lightning doesn't provide much information about the cause of thunder. For thousands of years, humans presumably noticed that correlation without being able to make any correct deduction about what causes thunder--Aristotle was probably not unusual in that he didn't connect thunder as an effect of lightning (he thought thunder was a result of the wind that occurred during storms). I remember as a child being told by someone that thunder was the sound of clouds slamming back to together after being split apart by lightning. The correlation with lightning doesn't inform one that was causes the sound known as thunder is a shock wave produced by the pressure of rapidly heated gas molecules. It's understanding the mechanics of the atmosphere, the nature of molecules in it, and actions of lightning that lead to understanding what causes thunder.
That sort of coherent explanation in which consciousness (intentions, beliefs, awareness, free will, etc.) is deduced as a logical consequence of the processes and components in the brain is what is missing in the hypothesis that consciousness is produced by brain matter.
One has to have more information than mere correlations in order to construct a causal model.
What correlations would enable one to rule out the hypothesis that consciousness is, like energy, a fundamental phenomenon, that brains are receivers and transmitters of consciousness?