Could not agree more! I think I have said before, for my school (and I imagine a lot of others), getting to an interview is a numbers game. A computer program 'works its magic' and spits out a list to interview (for those schools who interview). I can tell you we never open an application until we get that list, but meeting minimums is the minimum criteria for all items on the list and then all are ranked to determine how many we can interview based on how many slots we have. So for us a LOR or personal statement is not read until we have the applicants we are going to interview.
We have rubrics for LOR and personal statement and interview. Those are used, scored, and added to scoring for other things (GPA, GRE). We do not 'discuss' candidates at all; all scoring is done independently and then an average is taken. The rankings make our decisions, and during this, we are 'blind' to school graduated from, major, age, race, sex, etc. (the person interview probably knows all of this, but the AdCom does not). Our goal is to make admission decisions consistent, objective, and transparent. Our students tell us sometime we succeed they think, and sometimes we fail, but we have rubrics for everything, and a standard weighting equation.
The interview is where the applicant can convince the interviewers why PT is the right profession for them, what they will contribute to the profession, and how prepared they are or graduate school. All of that said, as DesertPT stated, this can vary school to school, although with the high number of apps many schools are getting, I cannot imagine it deviates much.
All of that said, a student-athlete in my opinion has one advantage that they should state in an interview or personal statement. With 20 hours/week plus study halls, meetings, etc. student-athletes have a lot of experience with time management and prioritization, 2 skills critical for a graduate student. Student-athletes are not unique in this (e.g., people who work significant hours), but for me, this is how SA status is different than other extra-curriculars; those you can always just stop if schoolwork gets stressful. So in an interview or personal statement, work it in somehow. HOW being a student athlete contributes, and not merely the fact that you were a student athlete.
Oh, and one more thing...as DesertPT said (seriously, you all should listen to her or him!), standing out is very, very difficult. ALL applicants want to help people, spend time with a patient, and have either gone to PT due to any various sports injuries or watched your grandmother/father, sister, etc. receive PT and saw the good it did. Every. Single. Applicant. Not a bad thing to say, but that rarely makes you stand out. In 8 years, I can think of 1 applicant that one of these things stood out (family member receiving PT), and I still remember the story to this day. But that is 1 out of over 200 I have interviewed, and many more personal statements I have read!