The statement that the ping 127.0.0.1 command can be used to check whether the network cable is correctly inserted into the host's Ethernet port is false because this command checks the local machine's IP stack, not the physical network connection. The statement that the ping command with the host's IP address as the destination can be used to verify that the TCP/IP protocol suite is functioning correctly is indeed correct and therefore false in the context of the question. The command 'ipconfig /release' is used to release the IPv4 address assigned to the device by the DHCP server; it does not check connectivity between the host and the local gateway.