Answers are slowly starting to emerge about the mysterious dongle the PS3 uses for wireless guitar capabilities in Guitar Hero III. The over-simplified version is that even though PS3 and Wii both use Bluetooth, the Wii guitar plugs directly into the Wiimote hijacking the signal, while the Sixaxis doesn't plug into the guitar -- hence the USB wired dongle as a wireless bridge.
Before we go any further, this isn't just a GH III problem. Rock Band will also use some sort of PS3 dongle. This might also explain a lot about why there isn't a Wii version of Rock Band announced yet. Although it's completely disputable, here's our basic idea: Two USB ports on the back of the Wii for the drum and mic (which are wired on every console), then if Harmonix wants the guitars to be wireless they need to design a guitar modeled around the Wiimote to plug into so that Rock Band does the same signal hijack that GH III accomplishes.
Apparently Sony doesn't feel up to talking about why these dongles are necessary as they stonewalled 1UP when the site went looking for answers. Maybe Sony will give Red Octane and Harmonix the tools to make their guitars work dongle-less one day, but to get things done for this holiday season this was the only (or most cost effective) solution available.
Update: We were trying to avoid bringing the Xbox 360 into this, but considering there is some confusion, the Xbox 360 version of Guitar Hero III is "dongle-less." Meaning a direct connection is made between the guitar and Xbox 360. Regarding Guitar Hero I & II support on PS3, Red Octane wrote us: "In regards to your other question about GH and GHII (on PS2), they do work on PS3 (w/ both SG and Kramer), though they will require an appropriate adapter for the guitar controller."