It has nothing to do with the “health” of the wine. By implication, if you had a white wine w/out that hue, would it be unhealthy? That would pretty much mean any white with age is going to be sick.
There’s not a lot of research, but there’s some.
From a Hungarian research paper on the color of white wines:
Their color is given by the flavones and the hydroxycinnamic phenolic acids in the grapes. “White” wine shades present a range of colors from white, yellow-white, green-white to yellow, gold-yellow, gold, green-yellow, depending on the yellow pigments given by flavones
Here’s from Oregon State U, Dept of Food Science and Technology:
In white wine, the most important phenolic compounds are the hydroxycinnamic acids and of minor quantities, the flavanol monomers. These compounds are important with regard to the visual quality of white wine.
So what are flavones? Here’s what flavones are:
http://www.liquisearch.com/flavones
They’re just compounds found in lots of fruits and vegetables; they provide yellowish pigments to the foods. Depending on when the grapes were picked, the amount of sunlight they received while ripening, the variety of the grape, the vintage, the fermentation and winemaking, etc., you have a shift in one direction or another from green to amber.
Some people suggest that the green comes from chlorophyll, since the juice of the grapes usually has some chlorophyll and even carotene. Since chlorophyll changes as the wine ages, younger grapes would be greener. That green fades as the wine oxidizes or ages, but that greenish hue is common in many whites around the world.
At any rate, the comment about “health” was just marketing.