[grand wazoo]

I live in an apartment complex and have an unsecured wireless router. It's not true, but would this be a valid defense?

I believe it is.

The existence of a router (secured or unsecured) make it impossible to track the download. Unless the download still exists on your hard drive.

[webstersII]

“The existence of a router (secured or unsecured) make it impossible to track the download”

Why do you say that?

If there is a router in your house, they just assume that the traffic went to a computer in your residence, anyway.