Canon mentioned battery life, focus acquisition and various other understandable facets can slow the shooting down to 4 fps. And yes, using a 500mm and a 2x TC to track a darting bird at 300+ feet would likely fall into that category. Please understand those two don't understand what they are doing, and sometimes give out terrible advice.
Some of the things from Canon's limitations for 12fps:
- Good temps are needed - 73 (seems limited)
- At least 60% battery (but doesn't completely stop the camera from fast shooting)
- Bad Batteries will cause problems (weak recharge performance)
- Wifi connections will speed it down
- Flicker reduction may slow it dow
- Shooting wide open is need for good light for AF/AE
- Obviously a good shutter speed
Anything other than a green H+ logo in the EVF will slow the burst speed down.