Unless I'm mistaken, not all Catholic institutions receive Federal monies, whereas the contraception mandate affects all them regardless of whether they do or not. Hence the BJU case doesn't serve as a model for this particular issue without some new law being passed by Congress. Incidentally, being beholden to Federal funds is precisely why a number of religious institutions were not happy about W's faith-based initiatives. They were concerned that if they became dependent upon them to do their work, a future administration would do something similar to what you proposed.
Right - I'm just talking about those which do receive Catholic money (which many of them receive some). But for those that do, is my interpretation of BJU v. US sound?