In my understanding a true red won't have visible undertones. In many reds you can see the pink, purple or orange undertones quite clearly, but true reds seem to have a perfect mixture of colors (often a hint of blue) so that when viewed in front of you there is no undertone. I think when people say true red they want no visible undertone. I've owned many Chanel reds and they only look red until held against a true red, in which case they look lighter or darker. I'd agree that 12A is as close to a true red as Chanel has been. I have a 14C and against the 12A my red looks strawberry.
To your theory, as a child sitting on a lawn, I closed one eye and looked at a blade of grass and saw a slightly different hue of green from one eye to the other. Perhaps we all perceive color slightly different. Time of day and angle of sun also matters. It has to do with the angle of the rays. Morning and evening light versus noonday sun. And the blue you.mentioned in a red bag means it is a cool red.