Stats are definitely not as important in psych as it may be in other specialties. Of course, they are part of the larger picture of the application, so it's more the consistency with the rest of your application that matters.
I've read a few applications on a review committee, and we generally look at everything a person has in their file, from which one can determine a certain proportion that will likely fit in well with the residency. Good letters and interesting personal statements really make an application stand out in my mind.
After you determine generally who you think would fit in with the program, the pool is narrowed down much further with the interview process. So I would say that interviews count much more in psych than they may in other fields. That's why there are so many more interviews (average 3-4, sometimes up to 5-6!) at psych places than, for example, medicine (where some of my friends had an average of 1-2).
Overall, though, it's much more of a "gut feel" than a scientific process, so my advice would be to apply to a range of places and not to rule any program out just because of stats.