Now, I might be an isolated example, but i have an i7-3770K + 2 7970, and i tell you in Battlefield MULTIPLAYER (not singleplayer), my CPU is bottlenecked.
Here are some of the tests i've done and some of the results, just to share (food for thought).
1. When I disable hyperthreading, and limit it just to 4 cores and run Battlefield 3 multiplayer (64 player conquest maps), i use coretemp to monitor my CPU temp + usage. When playing, all FOUR CORES are at 98-99%.
2. When I OVERCLOCK my 7970's, I GET ABSOLUTELY ZERO FPS GAIN (ie. i believe its CPU BOTTLENECKED since all four cores are at 98-99% usage).
3. Hyperthreading ON leads to same results in terms of overclocking (stock vs overclocked yield the same FPS, trust me i've tested this in many maps, different spots on the maps, stationary etc).
4. NOW, if i DISABLE CROSSFIRE and run ONE 7970 and overclock, i DO receive FPS gain (but obviously it is no where near the same FPS as crossfire).
5. By the way i have a 120hz monitor, which is why dual 7970 is actually required.
As you can see, i actaully have the computer and crossfire and first hand experience "bottleneck". Im not just someone going "yea i dont THINK any game would bottleneck a CPU" blah blah, so take my information with more than a grain of salt.