Auto insurance- should I add my girlfriend?

Im shopping around for insurance and have almost decided on Allstate because of the low cost on my two vehicles and renters insurance. My girlfriend and I bought a 2008 Nissan Altima two days ago and when I added it to my insurance it raise my monthly rates from $120 to $772, so I of course am shopping around frantically. The Nissan is being financed so it does require full coverage. My question is this; do I need to add my girlfriend on to my policy? When I asked for a quote with her as a secondary driver the man from Allstate asked if she lived with me and I said yes, he then said that if she has a valid drivers license from this state and my permission to drive the car she is fully covered under my policy, as long as the car is primarily in my name. I am the primary owner of the vehicle but her name is also on the title as secondary owner. That is what I am concerned about mostly. If something happened and it came down to the nitty gritty I want to be taken care of. Thank you in advance for your help and advice