Since MAC addresses are how equipment, such as hosts or computers on the network are uniquely identified, traffic going to and from a specific computer can be traced using the MAC address recorded in the log files. If you want to be anonymous on the local network, you may want to change your MAC address before you connect to a network, so that the network would log your activities using the arbitrary MAC address you self-assigned. Check out the tools section on the website on how to do this.