Actually you are right! Though this distinction seems to be disregarded in many forms of comics and other entertainment. Like how a lot of guys doing psychology work were considered psychiatrists in all those Far Side cartoons. "Psychiatrist" is just a sexier word, I guess.
And truth be told, in all honesty, Doctor V doesn't really do either of those things, she'll diagnose the problem, then it's off to whatever crazy, completely non-medical way there is to solve it.