You're absolutely right, shadowing is not a requirement. However, it's a great way to get exposure to the profession and confirm your decision to go to med school. All the faculty docs and fellows I've worked with had shadowed other physicians before applying, and as far as I know most of the residents had too. True, your family physician might be one who never shadowed, but he's at least familiar with it and might be able to help you get through the gauntlet.
Another way to get directly to the physician you want to shadow is to write a letter rather than calling. Unless there is someone screening mail, it's likely to be read by the right person. You could then call to follow up on your letter and the doctor, having heard your name already and knowing what you're calling about, is more likely to take the call.