"IP's are tied to MAC addresses"
This is not always the case. If you have a static IP address, you are correct, but if you have a dynamic IP address, there may be no correlation to the MAC addres. The MAC address is, however, always directly tied to the network card.
Regardless of static versus dynamic, the ip to mac correlation is always there. In the case of dynamic, whether or not it will be traceable will come down to a question of whether or not the dhcp server kept a log of all of its' transactions or not.