The Jabra BT620s was first marketed in 2006 and while that's a year before I started working for Jabra, I believe I know enough about the product, and Bluetooth products in general, to assist you. As I said, individual Bluetooth devices NEVER require drivers when connecting via Bluetooth - it's the device that brings Bluetooth into the PC that does. The only driver necessary would only be a requirement if you're connecting the BT620s to the PC via the USB cable. However, the product, since its infancy, has always been plug-and-play.
I'd suggest downloading the latest firmware here:
http://www.jabra.com/_gnimages/43a19110-c5c8-49be-a4b7-d06365709025/Jabra%20BT62 0s.zip
and updating your BT620s.
I'd check the USB cable - some cables are wired differently than others - more or less connections depending on their intended use (charging only, partial or full connectivity). Try a different cable to be sure. I can't answer why your PC is asking for a driver otherwise - it could be the cable or maybe there's something wrong with the headset at this point.
As long the device is functional, Jabra will support it.