I don't know why you're arguing. Whether they share parts or not is irrelevant. Toyota and Lexus are not separate companies. Lexus is just a different brand name built by the same company. It's not like Mercedes and Chrysler at all since they are 2 separate companies and one bought the other. Toyota = Lexus = Toyota = Lexus, they are the same. Not saying it's a bad thing, it isn't. It's just the way it is.
Sure they have a separate design and engineering team, but saying Lexus isn't Toyota is like saying owning a Chevrolet isn't owning a GM car.