'False color' is a post processing step. It doesn't matter what your source of the signal is, at some step when you make the image ready for human consumption (especially for web consumption), you get to decide how to map each of your channels to RGB (or whatever). When your sensors are RGB, then mapping directly to RGB makes sense. But you could swap green and red, and end up with a 'False Color'.

Remember, within each channel (doesn't matter how broad its frequency sensitivity is), the values you get are 'grayscale'.

Its perfectly legitimate to take multi sprectral data and collapse it down to gray scale (this is after all how we fake grayscale pictures taken on most digital cameras now).