Nah, probably not his CPU.
Here's an OLDER FX 6100 (* Bulldozer core = WORSE than 6300's Vishera core) compared to an i7 3770k showing the AMD 6-core more than capable of running BF3 maxed out.
http://www.youtube.com/watch?v=jV2Voo5h3eU
Could be something else. Maybe a chipset or GPU driver, even a BIOS update, holding either CPU,GPU or North Bridge back in some way.
Also, bear in mind even the Intel i7 3770k had a few dips below 60 FPS in the reference video. So don't panic if this happens once in a while.
* Also *
It sounds like your performance has dropped over time. If this was a gradual drop, could be dust buildup/heat issue... If this was a sudden drop, could be driver corruption, the above mentioned causes, or even a virus/malware.