Well, Toyota's also have a CAN-bus. And they pretty much work the same way now, since SAE decided the German Bosch protocols were the best. But anyways, the CAN system goes through the factory radio. The factory radio is just another module on the CAN.
Think of CAN as a LAN in your home or office (Local Area Network) in which all the PCs link together and communicate.
If the actual paired wires that carry the CAN data are not attached correctly (or bypassed) when a non-factory radio is installed, it can 'short out' the entire CAN bus, then the system cannot function properly and the modules won't be able to communicate properly with each other. Since the system can operate in 1-wire mode as a failsafe, most things will still work, but all the modules will be setting communications faults like mad, and some functions may be limited. You may also find a warning lamp staring you in the face. But keep in mind, not all modules can call for help, as they do not all have a warning lamp. The engine does (MIL), and the auto trans controller can generally send a signal to the engine controller to send a signal for MIL request to the cluster, so in a roundabout way, the TCM can call for help via the ECU too. ABS has its own lamp, SRS does, and so does the electro-steering (on cars so-equipped). But your CCM does not, nor does your audio system. That is where a scan tool comes in.
The CAN system has a CAN gateway, which is sorta like a router or switch on a LAN system, and it also is the liason via the scan tool to the other modules via the CAN bus. If you want to communicate via scan tool to the engine ECU, you actually talk to the CAN gateway, which in turn talks to the engine controller.
An aftermarket radio won't have any OBD intergrated into the car's CAN bus, so there won't be any communication with it, and various other modules in the car may set a DTC for "no communication with radio" but that won't necessarily cause any problems.
I hope I am making some sense....