Enabling all of the possible shipping types on the Quick Shopping Cart Shipping Configuration page does not necessarily mean that all of those shipping methods will be available for a particular shipment.
Quick Shopping Cart sends a Rate Request to your shipping providers containing all of the supplied information, and they send back a list of shipping types available (complete with rates) for that particular shipment.
For example, you may have selected UPS Next Day Air in the Quick Shopping Cart Admin Console; however, UPS may not respond with shipping information for UPS Next Day Air. This situation would likely occur because UPS Next Day Air is not available for that particular shipment based on the zip code for the delivery, the weight of the package, and the size of the package.
If a customer enters "00000" as the zip code, all enabled shipping methods display because this is an error condition for an invalid zip code.