Sigh this topic always comes up. From a materialist perspective (which is the only perspective that makes sense in medical science), yes, any psychological phenomenon is ultimately a physical phenomenon.

But when people talk about the psychological/physiological dichotomy, they're talking about causes. A psychological cause for an ailment is one that is brought about by thinking — by the brain operating normally without any external interference. A physiological cause is one that requires an external agent, like concussive force applied to the brain, or asphyxiation.

Psychiatric illnesses are an interesting edge case because they usually deal with the balance of various chemicals in the brain that are supposed to be there. That balance can be influenced both by external factors (like taking a psychoactive drug, such as an antidepressant SSRI) and by just thinking. It's not as well understood how thinking influences brain chemistry, but meditation, for instance, certainly does.

In a sense, they are. If we accept that the brain is what gives rise to our perception and personality, and to our experience of ourselves, then it stands to reason that all psychological phenomena arise from a configuration of the brain. It turns out that dumping chemicals into the brain can affect its configuration. But it doesn't follow that the new configuration leads to any more desirable psychological state than the old configuration.

Even if it were like that, things like the gut-brain connection (or rather, interaction) would destroy all hope for a neat separation of brain vs the rest.

That's crazy talk!