That is far from the truth! First off healthy is not always objective since carbs are healthy for most individuals but they're not healthy for diabetics. Gluten is fine for a lot of people but for someone with Celiac's disease it could lead to major health complications. You cannot just say something is healthy without specifying the context in which it's to be used.
Furthermore if one HAD to use HEALHIEST in regards to eggs, the most generalized statement (barring certain medical conditions) would be that the yolk is the healthiest. It has EFA's, vitamins A, D, E, selenium, folate, choline, calcium, phosphorous and many more micronutrients AND about half the protein. Tell me how whites are more healthy?? You're operating under the OLD belief that dietary cholesterol is directly related to serum cholesterol levels, this has been proven false many times over in many recent studies. Dietary cholesterol DOES NOT equal serum cholesterol. When you eat more cholesterol, your body makes less naturally, when you eat less cholesterol your body makes more naturally all in hopes of maintaining homeostasis. You do need some cholesterol (HDL) and you actually need LDL too, just not super high levels of it, in case you're unaware of that fact. This is in HEALTHY individuals. If someone has pre-existing cholesterol or lipid issues than yes, lowering dietary cholesterol can be a great thing. Out forth some evidence to back your claim as to why the whites are "healthiest". I'd be surprised to see if you can find even 1 or 2 solid sources of info that can't be undermined.