Just bought a 6D and a third party battery for backup. I've charged the original LP-E6 with no problem. However, the third party battery didn't charge even when I've done the same procedure as written by the OP. I've exchanged it with another third party battery and same thing happened. Finally, I've just added a some money and get another original.
Oh my, so you did just what Canon wanted you to do, amazing how this works esp. given the large price difference for essentially the same product. I seem to have been lucky, my ebay LP-E6 works fine in my 6D (I didn't unpack the new charger though).
I think it's important to look for offers that advertise "newest chip" or "work with newest cameras", as you can then return them in case it doesn't charge or isn't recognized.
Well, I think it's worth it I suppose. We're using several original LP-E6 in my part-time job/hobby for more than 4 years and they're still working and charging optimally while most of the third party batteries we were using as backups had failed already. I think it's worth it at the end of the day... but still, it hurts my pockets. Oh well, taking pictures with my 6D seems to ease up most of the pain. I can't define it but 6D IQ is a lot different from my 5D2 and Ti1 shots... Almost little to no PP is required. The metering and the IQ are just way ahead of those other two cameras. Ooops, sorry, can't contain my excitement.