I was never asked about OITE scores during my interview process for a fellowship, althought my results were listed on my application.
I believe that because the volume of applications are so much lower that it becomes more of a "who you know" situation.
Therefore, I think your letters of recommendations from faculty who are well connected will be your best option in getting the fellowship you want.
But it never hurts to do well on the OITE. It will keep the staff off of your back. I always read the most recent OKU and Miller review during the month before and did well each year.
