I have personally seen where there have been people who have left their entire estate to the BYU for use by the athletics department. You should be very careful to assume that there have not been donors who funded it to begin with.
I understand your point that the Church money didn't just generate itself, and to this I agree. I also agree that most of the money donated was intended for the "building of the kingdom." However, you should understand that not everyone defines the "building of the kingdom" the same way. Many people believe that the exposure that BYU football provides has a very positive effect on building the kingdom and have therefore donated to it.
My point to Zach Morris was that it is not all tithing dollars, nor did it all originate from tithing dollars. My point to you is that many donations were actually specifically donated for building the football program.