I read that "white" reference used for movie making is 6500K and since our eye adjust to set white point, 6500 kelvin ambient lighting would help make sure the white looks correct on your TV.

Any insight on this?

it would appear to be extremely "blue white" room lighting - most people would find it very odd. Easy enough to try an experiment.....get a couple of compact fluorescent lights balanced for daylight, 5500 to 6000 K, and try them. The human eye is a remarkable device, I really don't think you need to set the ambient light to match daylight just to watch movies filmed with "daylight" film.