Let me clarify -- if you don't graduate from a CAMPEP accredited program you will not be eligible to take the ABR exams UNLESS you attend a CAMPEP accredited residency program. After 2014, attending a CAMPEP accredited residency program will be REQUIRED. So right now if you graduated from a CAMPEP accredited medical physics graduate program you'd be eligible to take part 1 of the board exams without having to do a residency first, but not after 2014. Incidentally and if I recall correctly, the ABR also requires you to have taken certain physics courses e.g. quantum mechanics even though they are not directly applicable to clinical physics, so hopefully your BS degree is in physics. If it is not you might want to consider graduate programs that allow you to take the necessary physics courses as electives.
My experience has been that the CAMPEP accreditation for graduate programs is more or less a meaningless rubber stamp of approval since graduate programs very GREATLY in terms of which areas they focus on and the amount of clinical training they provide. You might decide you are better off going into a non-CAMPEP program that provides a lot of hands on clinical experience rather than going into a CAMPEP accredited program that is more research oriented.
I don't have any sense of what clinical residency programs look for in applicants but I will tell you this: of the three people I know that landed clinical internships only one had any direct clinical experience or research as a graduate student. The others focused on non-clinical imaging related research. And of the residents I know that were hired by my own institution, at least 2 did not have ANY medical physics background (Ph.d. in pure physics or bio-engineering, some post-graduate work related to medical physics). And now schools are beginning to offer a third route into the medical physics profession, which is the PDMP or Professional Doctorate in Medical Physics (a professional degree, sort of like an MBA). This is a degree in which you are typically required to have a Ph.d. in a field such as physics or bio-engineering and for which you pay a large amount of money (like the MBA) to acquire.
Finally, one more point. You didn't mention if the program you applied to is a Ph.d. or MS program. Typically, a Ph.d. in medical physics will make you more competitive for a residency even if your research work is not directly relevant to clinical physics. Many job postings now state that they prefer candidates with doctoral degrees.