Your problem is that MAC addresses can be spoofed.
If you use 802.1X authentication, this is no longer a problem. Provided that either you are using dot-1X or you don't care about MAC spoofing, then you need to record four things:
- The IP address of the access
- The time of the access
- Your DHCP logs listing which IP address was assigned to which MAC address when
- Who was logged in to which computer when
With these four pieces of information, and a list mapping MACs to computers, you can figure out which user was logged in to the perpetrating machine.
Note: to avoid IP spoofing, you must also use DHCP snooping and IP Source Guard to prevent users from giving themselves static IP addresses.
Second NB: this is operating under the assumption that all equipment connected to the network is company equipment. If this is not true, I suggest reading and logging the IP-to-port mappings from your switches, and recording them. That way you can tell where a computer was physically located.