I think the whole "connection" question is a tough one to answer. Everyone wants to be successful based entirely on merit, and as a naive undegrad, I joined that school of thought - if I am good enough at whatever it is, I will be successful. And for the most part, that is true. However, sometimes a foot in the door is not possible without a nudge in your direction. I have grappled with the idea of not wanting to compromise my beliefs about brown-nosing and undeserving sneakiness, and I don't think I would ever pull those kinds of strings. But many people I have spoken with - advisors, even admissions committee officers - have told me that there is such a large number of applications, and so many qualified applicants for medical school, that it is impossible to know what everyone is like even after interviewing them. Therefore, if there is some kind of personal reference, ie. oh, I know so-and-so, and they're a great person, I think they would do well in medical school, it certainly helps to distinguish that person from an equally qualified applicant that nobody knows. It is that way everywhere, especially when you are looking for a career. You don't have to ask everyone to vouch for you, but if you know people who would honestly put in a good word for you, then why not?