I can't speak to how picky they are, but I and at least one other member here went to Waseda's SILS through the CSU program (I was there 06-07). There are several other schools that have such arrangements with SILS, and the experience varies from program to program. As I recall, I had to write a short essay about why I wanted to go, fill out a bunch of paperwork, be interviewed and prove I could financially cover my expenses while I was there. I was up against a group of other applicants at my own school, and there were applicants from almost all the CSU schools to fill the 24 spots in our program, so there was a bit of competition, but it's hard to say what I said or did to get an edge over anyone else, aside from being sincere in my desire to study abroad, my interest in Japanese language and culture, and my eagerness to participate in the program.
Being fluent may make things easier for you while you're there, but それでも日本語の授業を受けることが必要だと思います。There's a placement test and even the fluent students had to take a minimum of high-level Japanese classes. Also, some caveats: unless things have changed (which I doubt very much): you will be restricted to taking classes offered by SILS, regardless of your language abilities, so don't bank on completing half of your GE requirements during your year there. Some credits may transfer as equivalents, but you need to check with your school. You may have to catch up, and even spend more time at your home institution to complete your requirements. Furthermore, Waseda is a prestigious school, but that doesn't really necessitate that the classes you take will be high calibur. Try to find out information about the professors to gauge how serious you'll need to be in their class. I had a few classes that I could call a breeze or just boring, and some that were very engaging and challenging, it all depends on the teacher. A lot of students treat their year abroad as a vacation, and in my program, our grades were actually bumped an entire letter grade when they were transferred back home, so there wasn't a whole lot of incentive to apply ourselves (I did anyways, for what it's worth).
Hope that helps, let me know if you have any specific questions