A Live CD session operates entirely in RAM with no hard drives mounted, unless, the user mounts them. Typically, a router can be turned off while the Live CD boots into RAM, and then any changes made prior to turning the router on thus enabling the Network connection.
Contrary to common belief, the Live CD session can Disable the Network connection, mount a hard drive, and any downloaded files can be saved to the hard drive, then the hard drive can be unmounted, and the Network connection re-enabled.
All installed OSes by definition expose the hard drive to the Network because the installed OS needs to reference the hard drive for programs to execute and the like while a Network connection to the Internet is active. This is not true of a Live CD session where the Live CD is read-only, and executes entirely in RAM with no hard drives mounted during the session.