Good observation! When a potential employer says, "Tell me about yourself," it's important to note at what point in the interview s/he has asked the question.
It's sometimes used by an employer to break the ice. If the question is asked at the top of the interview, keep your answer strictly professional. It's a golden opportunity to touch upon what you think are the highlights and strengths of your work experience. Don't brag, stay off your soapbox, and don't badmouth anybody. Giving a response that is attention-getting breaks the ice, and opens the door to further questions about the positive aspects of yourself and your work.
But then there's the situation like you experienced, where the question is asked later in the interview. At this point, the interviewer is likely looking for something different. Since they've probably already asked you to elaborate on your skills and experience, now they want to know about you. They want to know about your interests and interpersonal and communication skills outside of strictly work-talk. Aside from clinical and/or technical skills, personality fit is a major factor in a hiring decision.
Discuss your interests and your values. Be yourself, but in a good light. Even if your main recreational activity is attending wild parties, it would be a good idea to translate that into something more tame, like "going out with friends." Maybe you enjoy baseball or soccer, and maybe the hospital has a Social Committee that sponsors one of these teams. Maybe you've traveled. Maybe you're fluent or near fluent in a second or third language. (Maybe you're an expert baker who loves bringing samples to work!)
As for your values, maybe you're into personal development and are constantly taking courses. Maybe you love helping people and regularly do volunteer work. Maybe you want to get into management in the future.
The later timing of the question gives you the opportunity to let the interviewer see the personal side of you, and make you stand out from others with similar experience – and therefore convince the interviewer that