For the Nestle claim - sources differ. Some say they were manufacturing it as early as 1930. Others say the introduction of the Galak bar (known as the Milkybar in the UK) in 1936 was the first. Still others claim it wasn't really white chocolate until the 1948 Alpine White Bar, which contained almonds. This article indicates that Nestle's research into a coating for a children's vitamin was what birthed white chocolate.
Still, it did seem a little unusual that white chocolate was developed so late (even though milk chocolate wasn't really a thing until the 1890s). So I did a little digging. There wasn't a whole lot out there. Most of the hits were for the words "white" and "chocolate" that just happened to be next to each other. I got excited by a reference to "white chocolate cake" from the 1870s, but that turned out to just be a white cake with chocolate frosting. But then, I started to find some interesting tidbits.
White Chocolate Skepticism, 1916
I did find another reference, several years later, in the 1923 Encyclopedia of Food by Artemis Ward. In the entry for "Cocoa-Butter," the main text is followed by this little intriguing sentence - "Swiss 'white chocolate' - apart from milk-chocolate types - is cocoa-butter sweetened either with sugar or with sweet chestnut-meal."
A tantalizing snippet, unreadable in full (thanks, Google Books), indicates this description in Food Industries Manual published in 1931, on page 142: "White chocolate is manufactured from sugar, milk powder or condensed milk, and cocoa butter, and the flavour of chocolate is dependent upon the cocoa butter content. Accordingly a very strong cocoa butter is used in the manufacture ..." and that's all we get!
Still, we're definitely pre-dating the Nestle story.
And then there was this strange little find.
Strange White Chocolate, 1870s
A similar recipe shows up in a druggist's recipe book from 1871.

White Chocolate Caramel Tablets, 1869
The Broma Process, 1865
The timeline certainly matches the above findings of pre-1930s white chocolate.
The Zero Bar, 1920
A caramel nougat with almonds and enrobed in white fudge, this candy bar appears to be one of the earliest commercial applications of white chocolate.
Today, the Zero Bar is still manufactured by the Hershey Company, although it can be difficult to find in stores.
White Chocolate Conclusions
I personally enjoy white chocolate, and the Zero bar was a childhood favorite of mine, although I know many people think white chocolate is inferior to the kind including the whole bean. But I'm not sure I enjoy it quite as much as these Alpine White television commercials would have us believe.