Yes, I would drop my medical malpractice lawsuit if the doctor gave an apology and explanation. In most cases, I and many people, understand that simple mistakes happen everywhere. More than anything, we're looking for reassurance that the doctor is aware of the problem, and has taken steps to prevent it from happening again. The purpose of a malpractice suit then is only to force the doctor into such a position.
Sometimes all people want is an explanation, and an apology. Doctors are human and make mistakes just like the rest of us. They are often so busy, that patients don't feel they're getting full attention from a physician or surgeon. However, there are some actions that can't be apologized away. True medical negligence or egregious conduct that's outside the realm of tolerance can rise to a level that won't make a lawsuit anything other than a certainty, even with an apology.
If a doctor could get away with medical malpractice just by offering an apology, she would have no incentive not to commit malpractice again. In addition, an apology doesn't compensate the victim for the losses they have suffered. The person might need additional medical care, and an apology isn't enough to pay for it.
An apology and explanation are nice, but they do not help me recover from the injury I sustained at the hands of the doctor. Medical malpractice suits help patients recover the money they lost from their injuries or funeral expenses and lost wages from a death and keep bad doctors from practicing medicine.