Your theory has already been debunked, but here it is again.
I don't have a white car so I took a panel I cut from a white car and added some chrome wrap, angled it towards the sun:
Measurements taken from the underside:
Optical:
IR:
So two degrees cooler than white. Now if my cars were white, I wouldn't bother, but bright green already shows a 10-15 degree improvement, and black and grey show up to 60 degrees.
We use chrome wrap to insulate buildings in hot conditions, car window foils are chrome etc. It really shouldn't be controversial. We actually WANT high reflectivity and low emmisivity:
If we can reflect 97% of the IR energy, we don't really have to worry about the emmisivity of the remaining 3%.