Som buzz words in the insurance business are "primary" and "secondary" and "loss of use" and "diminution of value".
"Primary" means they pay first, according to their rules. If you buy the rental company coverage it is primary.
If you use a credit card with the feature (except some Diners Club plans) that is secondary. Check the credit card's rules for car rental insurance benefits. Your own insurance would be primary and you are subject to surcharges as if you had the accident with your own car. (The credit card, being secondary but whose rules include the first $500. or so, will cover the deductible which by definition your own insurance company does not pay according to its rules.)
Your own insurance company and/or your credit card may or may not cover loss of use which amounts to extra rental days charged to you while the car is in the repair shop.
You may be charged diminution of value if in the opinion of the car rental agency the car won't sell for the anticipated price because it has been in an, any, accident, yours. Almost all rental companies sell or auction off the cars after about two years.
Some rental offices in the U.S. require that non-US citizens buy their coverage. Check the rental company's rules, generally available on their web site and also on Travelocity.com if you book on line.
Disney hints:
http://members.aol.com/ajaynejr/disney.htm