Thanks for the reference.  I found it before I entered this question because I could not trace any authoritative sources. 

I just got off the phone with a representative from the health care sharing organization in question that I called to find out if they had any authoritative information that would be helpful.  Their representative basically rebutted the answer I was hoping to hear by stating that the position of their organization is that the monthly payments are "gifts to other participants" and therefore are not medical payments, nor are they deductible.