Well Yes and No. A Pediatrician is a medical physician with a specialization.
While you really must have a 4 year degree, you cannot get a medical degree or be a Pediatrician with just a four year degree - from any school. It takes much more schooling.
Getting a Medical degree requires going/graduating from a medical school. That is a many years program done after college. Once one gets their Doctorate degree, they then need to take certain programs...it becomes more a hands on thing than you may consider school at this point...in that specialization. Additional to getting the degree's you need is to pass certain professional tests to be certified/licensed so that you are actually able to work in the field.
Like anything there are exceptions, but in the very competitive field of medicine, for a Medical school to accept you it is best to have gone to a 4 year (or undergraduate) college at an institution of high regard...not just any school, AND to have taken a specific course of programs preparing one for medical school. Generally in the Sciences. (So, just going to a great school and getting a four year degree in say Accounting, won't eliminate you, but it isn't really going to lead to you being very desired by a medical school). There are also entry tests, similar to the SAT in high school, that the medical schools rely on. Basically aptitude and knowledge based, to identify people who have the inherent ability to be a physican.