The Nikon batteries are made by Sony. I have a spec sheet from Nikon on the D7000 battery that specifically references Sony Battery company.
There are "does it operate" and "how long does it last" questions. The newer batteries have electronics to communicate with the camera about battery life, charge level, number of images, etc. Third party batteries should have that information - but you need to verify it. The battery also communicates with the charger and prevents the battery from over charging and reducing life. If the battery gets too hot in charging, life is significantly reduced. I would monitor third party batteries for a while and make sure they don't overheat or sit on a charger too long.
The second issue - battery life - can be more of a factor. If the battery is half the price but has one third the life, is it really cheaper. My experience is that third party batteries have a significantly shorter life than the Nikon batteries. I've purchased 4 branded third party batteries from a reputable source and all failed within a year or two. I've never worn out a Nikon battery - even batteries from my D200 in November 2005 are still operational.