Every treatment for every mental problem no matter how small is in reality a chemical treatment. Boyfriend dumps you and you're sad it's a chemical problem. But a nice bowl of ice cream or what ever you do when you are sad and moving along to find love again is typically a better treatment than pills and it is still essentially a chemical treatment.
We live in a physical world. Many people fallaciously think chemicals are involved so use chemicals (synthetically produced recent human inventions). It sounds like it makes sense and they have their place, but we should be using tried and true treatments such as talking to someone before resorting to newer treatments which even if they've passed clinical trials can sometimes turn out to have unforeseen problems.
Talking to a counselor has even been tested and it's found that chemical changes occur in the brain from it. Not only that but depression patients relying exclusively on talk therapy would become depressed again on average 1 year after seeing a counselor. Those relying exclusively on pills became depressed again on average after 2 weeks.
No, a chemical problem in the brain and a problem that isn't chemical is not a false distinction, because the causes of the two problems are significantly different. A person cannot hope to understand how to solve a problem without first understanding the cause. A brain imbalance is treated much differently than a sprained ankle.
No, a chemical brain problem and a non-chemical brain problem are not a false distinction. In one case, a problem can be identified as chemical in nature, and in the other, a problem can be identified through some other means, such as a tumor. Thus, this is not a false distinction.