Mostly agree. When you say it doesn't matter if the compressor is on or off, could you describe in more detail how you turn the compressor off? If you're in defrost or recirculate mode, you can't turn the compressor off.
You might also raise the hood and watch the front of the compressor. If the idle jumps up and down as the clutch engages and disengages, that's the real proof it's a dirty throttle body.
Welcome! And you might also share your model in your profile (so we can confirm it's an I6 - V8 models don't usually have this problem) and how many miles. Usually the dirty throttle body syndrome doesn't show up until the owner has a battery failure or disconnection, which resets the memory in the PCM and the computer has to re-learn the throttle body behavior all over again.