Some people might like looking at RITE scores, but I'm not one of them. For people going into stroke or NCC, practice-based experience carries more weight. If you've done a bunch of ICU rotations, and been giving tPA without much backup for several years, then I know you can at least sorta do the job when you show up, at least well enough to take call without having a coronary event. The rest we can teach. Remember that fellowship is still about learning, so you're not expected to come in fully-fledged. RITE exam scores may predict board scores if you believe the people that get paid to administer them, but someone who studies hard for the boards and gets a top percentile score isn't a better doctor -- in fact, they probably need some remediation in time management.
It's more important that you've done enough to know this is what you want for your life, and that people have been impressed with your enthusiasm for the field. Research is fine, but most people don't have that much, aside from the PhDs, which is an unfair comparison. Letters can carry a lot of weight, although we also sometimes have personal conversations as well, which sometimes paint a quite different picture than what appears in your letter. In all honesty, it's usually pretty clear who the top applicants are just from an overall picture painted by their applications in toto.
For some other fellowships there might be more emphasis on RITE scores and such -- I don't know how epilepsy and neuromuscular fellowships rank their people. They get a lot of applicants at the major programs, for few spots, so they might use scores to substratify them.
