6-10 years? No, not true at all. I was accepted to Fletcher, SAIS, SIPA, etc. and certainly didn't have that much work experience, and neither did the majority of my classmates. To the OP: 2-3 years (ideally overseas work) should serve you fine. Yale or Chicago CIR might take you right out of undergrad, but the question then becomes how much you can really get out of one of these programs without work experience. If you want a more academic program, if you are looking for a pre-doctoral Masters or something, then you could be fine right out of undergrad.
Why do you want to attend a grad IR program?