Blood Brain Barrier:
We're not talking etymology, but the use of the word, in public use, as a title. When I have a column called "ask Dr. Blood Brain Barrier" with no more information there is the assumption that I'm a physician and not a lawyer, physiotherapist or priest no matter what qualifications I have. I don't know where you live but it would have to be a strange place for that not to be the case. End of story.
You can go on simply insisting you're right, but it's not providing your case any weight whatsoever. If I make mention of "Dr. Freud," no one wonders if I'm referencing some obscure gastroenterologist. And while I think the guy's a hack, "Dr. Phil" has never been confused with a pediatrician.
Now, I can certainly agree that, nine times out of ten, when people say someone is "a doctor" without any kind of qualifier, they're indicating a medical or psychological doctor. I can also agree that medical doctor is more often the intent. But that's not what we're debating here.
The title of doctor requires only one thing: a doctorate in a particular field. That is, in fact, why it is called a doctorate. It's perfectly correct for Dr. Mark to call himself Dr. Mark. Why? Because he is Dr. Mark. And no, he doesn't have to append PsyD to his name to be correct.
Now, to avoid confusion, most Drs. do tend to add the type of doctor to the end.
Dr. Smith, DDS.
Dr. House, MD.
Dr. Johnson, Ed. D.
And also when someone asks me what I do and I say "a doctor", it should be obvious the meaning of the word isn't intended to be "someone who is master of something". That would be a ridiculous and pointless reply giving no information as to my profession.
Colloquial use of a term doesn't negate the meaning of the term. It just means in certain cases, more context is expected because of certain assumptions. What's more, you're not talking about a title anymore.
If someone says, "I'm Dr. Campbell," that's a correct use of the title regardless of what their doctorate may be. If I say, "I'm a doctor," instead of "I'm a doctor of music composition," I'm not providing enough information. I'm misusing the colloquial understanding. What I'm saying isn't incorrect, but it is unclear and ambiguous in many situations. Having the title of doctor, and saying you're "A doctor" have different connotations, but neither is correct or incorrect universally.
Dr. Mark is Dr. Mark. He's a psychological doctor. His title is perfectly fine to use, because it is 100% correct and accurate. Now, if he was just running around saying, "Trust me, I'm a doctor," you could argue he's being deliberately misleading.
Let's get this "title" business out of the way, since it's not even the original point: If all this was completely true then medical professionals who don't have a doctorate but are entitled to practice medicine wouldn't be called doctors. Claiming that medical doctors can't call themself doctors because they don't have a doctorate is beyond silly, especially when the primary definition for "doctor" is "a person who is qualified to treat people who are ill" (Oxford dictionary). I go to my GP all the time. He's called Dr. (name), but doesn't hold a doctorate. How does that work?
What this tells us is that it's the way that we use words that matter, not correct usage. It's neither correct nor incorrect to say "I want to see the doctor" when the person concerned doesn't have a doctorate, because it's understood that you want to see the medical practitioner, and it's been understood that way for many hundreds of years. Now when you go see a lawyer you don't say "I want to see the doctor" - though that may be strictly correct because he holds an LLD, it's simply not what is said in common usage. Try going to your local lawyer's office and say that line to the receptionist. If you don't get any confused looks, then I'll yield to your views 100%.
The bold part of your post is all that I was ever saying. It seems we don't really disagree after all.