I am certainly not a networking pro but you seem to have a few things mixed up. NAT is sometimes confused with proxy servers, but there are definite differences between them. NAT is transparent to the source and to destination computers. Neither one realizes that it is dealing with a third device. But a proxy server on the other hand is not transparent. If you are using a proxy server then yes you must do some configuring.

As to your question "never wondered why you didn't have to 'dialup' with a cablemodem ?" As a matter of fact no I did not wonder because there is no 'dial up' because unlike a telephone line the cable connection is never disconnected unless you physically disconnect the coaxial cable itself (or turn the router off).

A cable modem (which isn't really a modem at all) is NOT capable of NAT, it is only the link between your pc and the network.