Mac spoof paranoia: Who impersonated me system?

I’m a little confused, and I’m concerned.

The system I use at work is wired, not wireless. But I’m pretty much ignorant about networks beyond that.

a. Could someone on the same network spoof my mac address and use it?

b. If (a), then how do I prove the log file showing my comp visiting one of _those_ porn sites is patently false?