Received my USB link cable (aka "SilverLink") yesterday. I can now confirm that it does in fact work with TI82 and TiLP 1.6. So, no more fiddling around with dodgy parallel/serial cables.
In order to use the USB cable with TI82 (and the other supported TI calcs as well), make sure you
1) Install TiLP 1.6 or up, and the included SilverLink driver, before plugging the cable into your computer for the first time
2) Do not install any official TI connectivity software, it will not work and will mess up the TiLP install.