The answer depends on which policy you purchase. If you purchase a limited coverage plan, you may still have to pay the difference since such policies have limits on how much they will pay for a particular service you take.
If you have a comprehensive coverage plan, you may be responsible for co-insurance, which is usually 0-20 percent of up to the first $5,000 and the rest is paid by the insurance company. If you want to keep your liability low, a comprehensive coverage policy is preferred. Here is some more information: Visitors Insurance: Comprehensive Vs. Limited Plans
Insurance rates are regulated by law. You can't find the same insurance plan for a lower price anywhere else