Methodological naturalism and metaphysics.
Medical science recognises psychogenic pathologies, that is diseases whose causal origins are entirely mental, and medical science also recognises diseases of entirely physical causal origin, for example those occasioned by poisoning. In other words, unless there is a well motivated independent reason to quarantine medical science and hold that it does not employ methodological naturalism, science implies property dualism, at least.
Accordingly, as both idealism and physicalism are inconsistent with dualism, each of these implies the supernatural. However, the idealist needn't be committed to naturalism, so this problem only impacts the physicalist, as the truth of physicalism implies the truth of metaphysical naturalism.
To be clear, I am not contending that methodological naturalism implies metaphysical naturalism or vice versa, only that science, and therefore physics, does not support physicalism. In fact, physics, as a science, supports the falsity of physicalism.