The latest issue of Nature Medicine has several short articles on patent issues, and is well worth a look if that's your sort of thing. I enjoyed this from the issue's lead editorial:

"An informal poll we conducted while preparing the focus on patents appearing in this issue (pp 1239–1243) disclosed that about two-thirds of scientists, particularly in Europe, don't know who owns the intellectual rights to the discoveries made in their labs. A similarly high proportion don't know if there are any provisions in their job contracts assigning them any rights over their discovery. And roughly half don't even know whether they are legally entitled to open a company based on their research."

As the piece goes on to explain, these turn out not to be particularly hard questions to answer. They are, in fact, answered in just the way you think they are, which makes me wonder a bit about the people who don't know these things. Let's see, even though you're not a lawyer, and don't know much about these things, and you're signing an agreement with a large entity that's very interested in this subject and can afford to pay for good legal advice about it. . .hmm, I wonder who could possibly have the advantage here?