If a notarized piece of paper would instantly absolve you of any further investigation by the police if you were driving a vehicle you were not the registered owner of, all car thieves would have one. Driving a vehicle loaned to you is common, and in America you aren't going to be stopped and questioned by the police unless you are doing something suspicious or illegal (regardless of what some people with a real police phobia will post). If it all comes together, enjoy your trip, the US is a great country to explore.