Although I have not been sued myself, I have colleagues who have been named in lawsuits. Believe me, if the doctor or the hospital can point the finger at you to keep themselves from paying through the nose, they will. You need to have something to protect yourself and your assets, not to mention the assurance you will be able to afford your own lawyer, if needed, as the hospital counsel will watch out for the needs of the client who is PAYING them before the needs of the nurses they are also representing under the hospital's malpractice insurance. Besides, look closely at your handbook: you're covered by the hospital malpractice insurance only if you are performing within the scope of your job description. So if you do something that might be considered outside your scope of practice, the hospital is completely off the hook and guess where you are? Hanging out to dry! In areas such as critical care and ER, sometimes you do things that could be considered practicing medicine without a license, in which case, the hospital just says, "too bad, you should have stayed within your job description."
I don't mean to sound scary, but I will protect myself. And it doesn't cost that much.
BTW, we were required to carry our own student malpractice insurance in nursing school.