Remember....they just dropped a 1.5 BILLION dollars into downtown SLC for the City Creek Center. No tithing funds were used for that project. Zero, Zip, Nada. I don't see them straining at all if they wanted a medical school.
There is a business side of the church few people pay attention to. They have huge land, agricultural and livestock holdings throughout the United States. Tithing is great, but it is not the only source of money they have. When you can throw 1.5 large at a mall in SLC there is certainly enough money to build and support a medical school.