If all else were the exact same, I think you would be right. People would tend to pick the doctor with the better pedigree. If all else were equal. The problem is, all else is never equal. If you're picking doctors by just looking at where they went to med school, you're not going to end up doing very well. Might as well flip a coin. Most people will look at other things and even ask around to see if people they know and trust also trust a specific doctor. Word of mouth, trust, and bedside manner go a long way. If you ask people if they'd rather have a Harvard-educated doc who's an ass or a state university-educated doc who has great people skills, they'd probably say the latter.
Which brings me to my second point. Med school is not a good indicator of physician competence or interpersonal skills. A better indicator is where they trained and how other patients view them. You could very well train at Harvard and end up at a mediocre residency program in your field. Or vice versa.