I don't know other aproaches, although I think there are many...
You have to check a few things:
• The red channel must be the bigger, as you suggested, but you must ensure it has a considerable gap between it and the other channels. The color 255, 254, 254, for instance, is mostly white, and not red.
• The other two channels must be balanced, as it will change the color if you have one of them bigger than the other. 255, 150, 0 is orange, and not red. 255, 150, 150 is light red.