This is one of those "damned if you do, damned if you don't" situations. The hospital is just trying to stay in compliance with HIPAA and the various personal non-public information regulations. Their solution DOES seem a little overboard, but this is what happens when people continually lose laptops/usb drives/etc that contain sensitive information. While this might be a little hard for the hospital's employees to get used to, it's really a win for us normal folk (assuming it's all properly executed, which is a big assumption).
As far as legal recourse, IANAL but I don't think you really have one. While I get the whole "You're not touching my computer" bit, why don't you just use the computers provided ? Hell, even at the community college I go to, I have to install some software just to connect to their network. Same with some of the other corporations that friends and family work for. In the end, if you weasel your way around the restrictions and then lose your laptop, have it stolen, whatever - you'll really be on the hook.