And let me word it a bit differently to clarify that for anyone that doesn't understand. The antenna is grounded to the body of the car at its mounting point, which grounds the shield inside of the coaxial antenna wire. This grounds the outside of the plug at the head unit, which internally all of the grounds link together - but together does not mean equal!! ALL of the grounds in your car link together at some point, but you woulnd't use the ground from the tailight to ground a 1000 watt amp right? Exact same idea here. Ground everything properly and much less trouble will be had in all of your electrical systems!
Glad to hear your tunes are working now!