Uploading or downloading works protected by copyright without the authority of the copyright owner is an infringement of the copyright owner's exclusive rights of reproduction and/or distribution.
Several exclusive rights typically attach to the holder of a copyright:
- to produce copies or reproductions of the work and to sell those copies (mechanical rights; including, sometimes, electronic copies: distribution rights)
- to import or export the work
An item is considered an export whether or not it is leaving the United States temporarily, if it is leaving the United State but is not for sale (a gift), or if it is going to a wholly owned U.S. subsidiary in a foreign country.
(I personally think this is all bullshit when applied to the Internet, but my opinion doesn't matter.)