The FX6350 is a Vishera, theoricaly 125W but actualy much less , so there can be a peak current limitation since the MB support up to 140W, wich include all FX83xx but thoses latter may have higher peak currents than Phenoms, Gygabyte may have tested a few SKU and concluded that it was cautious to limit it to a 6C...officialy.
That said the board could work with a regular FX8320 or 8350 if not overclocked but one more time it s not guaranted at all...
Edit : Latest bios was released 5 months before Vishera....