My understanding is the church pays roughly 70% of the bill. Given annual tuition is 5,500 for a full year meaning the church puts out about 12,750 per student per year. With Approx 30,000 students I would expect the outlay to be 380 Million a year. A huge number, no doubt, but 40% of the number quoted.
1 Billion would imply that the church is paying 86% of the bill. It is possible, but it goes against the numbers that were presented in various meetings I have attended.
Furthermore, the church commissioned an extensive study in the late 90's to determine whether the investment was worthwhile. After the completion of the study, not only did the church not decrease the expenditures to support BYU, but they expanded Ricks to a 4 year college and dramatically increased their enrollment. I have heard second hand some of what was in that report, but the Ricks transformation is the biggest indicator of the findings in that report and the weight the brethren give the return on those tithing funds