It's not a postal thing, I believe it's common law. If someone ships you something unsolicited, you are under no obligation to return the item or make payment.

Aha! "Unsolicited" was the missing piece in the Google puzzle. It's actually not common law. It's 39 USC § 3009: http://www.law.cornell.edu/uscode/text/39/3009, and was passed in the Postal Reorganization Act of 1970.

I believe this was originally in response to shoe manufacturers mailing people shoes and then invoicing for them if they weren't sent back.

As for whether it applies to non-USPS shipments, I have strong doubts. The law says "mail", and my understanding is that because the USPS is a protected monopoly, non-USPS carriers are explicitly not mail services.