Limiting current from a 5v power supply
I'm trying to build a DIY Xbox Kinect adapter to be able to plug the Kinect into my computer, but I'm getting some shaky information. From what I've seen, the official Kinect adapter (for using the Kinect with an non-slim Xbox 360) outputs 1.08A @ 12V. I've got a power supply that outputs 12V @ 3A and I need to know whether using this will damage the Kinect.
My understanding is that a circuit will only draw as much current as is required for it to operate. For example, I can connect an LED that requires 20mA @ 3.3V, in series with an 85 ohm resistor, to a wall-wort power supply that outputs 850mA @ 5V. Computer PSUs generally have a 12V rail with as high as 50A. I could plug a hard drive into one of those rails (as the only load on that rail) and nothing bad happens, and I guarantee that the HDD isn't drawing 50A.
At any rate, am I correct in assuming that using a power supply rated for a higher current won't damage the circuit, as the circuit will only pull as much as it needs?