Wouldn't that be easy to foil? I can, and do, write with different styles that depend on the audience I'm trying to reach. I'm reasonably sure I could write entirely unlike my normal writing and appear to be a completely different person. I've done a lot of writing for very different audiences.
Am I, perhaps, over-estimating my ability? Are they really that good at determining origin?
And the motivation to dedicate resources to this is...? You already fired the person, what does it matter if you find out who they are?