How are letters of recommendation handled when they come from a member of the admissions committee?
I've seen this situation.  In our department all faculty vote on admission decisions (we don't have a separate committee that is delegated to make these decisions.)  The faculty who have written recommendations have typically argued in favor of admitting the students they've written recommendation letters for, but it would also not be surprising if a faculty member who recommended a student felt that other candidates were better qualified when it came time to make final decisions.   

It's one thing to say "I think student A is well qualified for our graduate program and a TA." This is not inconsistent with "After reviewing all of the candidates, I feel that students B and C (with BS degrees from elsewhere) are the most deserving of the two available TA slots." or even "After discussion with other faculty members, and reading all of the recommendation letters, I've agreed that student A should not be admitted to the program."    

It's important to understand that these are group decisions, and that faculty committees often operate by discussion and consensus rather than by simple vote counting- a lot can happen during such a discussion.  

As an applicant, there really isn't anything that you can do about this- the faculty in the department will deal with it as they choose.