The stories are true. This is in fact how things are done.
One person posted a video of a Hermes bag, showing the entire factory where the bag was being made, showing all the steps in the process from raw materials to the finished product, and stating that the actual cost of making the bag was US$1,395 while Hermes sold the bag at retail for US$38,000. The man in the video said "Why don't you just buy it from us for US$2,000?" Many people have done precisely that, and millions of people who have watched these videos are in shock to learn the truth - that Chinese factories manufacture nearly all the very expensive so-called "luxury goods" at very low prices and that consumers are spending 90% of their money for the brand name.
When this news broke, one or two of the large European fashion houses disclaimed it, saying "That's not true", but offering no evidence beyond that, while all the others merely went silent. One European brand published a short video which attempted to contradict the claims, but the video showed only a few designers around a table, working on the design of a new product. Several people immediately posted videos demanding that the European fashion houses produce a video showing the actual factory in Europe, with the thousands of Europeans sitting at sewing machines and stitching a handbag, asking to be shown the factory actually producing the entire product. No fashion house replied to that demand. Nor could they.
The fact of these luxury items being fully manufactured in China but then carrying a "Made in Italy" label is of course fraudulent, but international IP laws and trade regulations permit this to be done, and so they do it.
But this is both different than you might imagine, and also worse than you might imagine. I will explain. Several Chinese cities, Shanghai among them, has what is called a "Free-Trade Zone". This is a bit complicated to explain, but a free trade zone is a kind of diplomatic no-man's land. It is physically within Mainland China but is treated for customs and foreign trade purposes as if it were a separate sovereign entity. Think of it as a kind of "offshore island" near Shanghai.
These zones were created to facilitate various kinds of foreign trade and to eliminate certain kinds of inconveniences in trade. In practice, a foreign company can ship goods directly into Shanghai's Free Trade Zone without incurring customs duties of any kind, and can freely ship these items out again without restriction, so long as they do not enter Mainland China when they leave the free-trade zone.
What happens in real life is that many of the foreign luxury brands will have their products made by a factory in Mainland China, then ship them not to Italy or France but to Shanghai's Free Trade Zone. It is there that they will perform the final touches, affix their logos and tags, and do the packaging. They then ship the goods out of the free-trade zone back into Mainland China, now bearing a tag that says "Made in Italy". Thus, the entire manufacturing process, including the affixing of the "Made in Italy" tag, is done inside Mainland China. There is no need to send the goods to Europe for the final touches.
There is one more related item that I should include here, and that is the recurrent accusations of China making and selling "counterfeit" and "fake" brand name items. I'm sure some of this does occur, but much less than you might imagine, and the truth of these "counterfeit" accusations is far from chaste. Again, I will explain.
European fashion houses (and most American manufacturers of consumer goods as well) do not have their own factories in China. Instead, they find a Chinese factory to produce their product according to rigid specifications. This is sensible because they avoid the cost of building their own factory, training their own staff, and creating their own supply chains. So far, so good.
But there is a catch. The European brand will ask a factory to produce, for example, 100,000 ladies' handbags of a particular style. Every factory knows that in volume production there will be a small percentage of items containing flaws. This could be from the original materials, a hand slipping on a sewing machine, or a dozen other causes. And that means that a factory will slightly over-produce because quality control is very high and items containing even the slightest flaws will not be accepted. In this example, the factory might produce 102,500 bags, 2,500 extra, representing a 2.5% rate of flawed items.
But when the production run is completed and the quality inspections have been done, the factory discovers that only 500 handbags contained flaws. What do we do with the extra 2,000 bags? The fashion house will pay for only the 100,000 it ordered, but the factory cannot afford to simply discard the excess production because the cost represents a large part of its profit.
You will have already guessed the answer. The factory sells off this excess production to shops on Taobao, to various wholesalers, and even to street market vendors. I know, because I have followed this process from start to finish and have purchased some of these items from the street markets. These products are not "counterfeit" or "fake" in any sense. They are 100% legitimate brand-name items, representing excess production of the original brand item.

I am pleased to see the truth of this luxury-goods manufacturing escaping confinement. Consumers truly are being taken advantage of in so many ways, most especially in paying a markup of tens of thousands of percent for the privilege and cachet of having a "brand name" product. It is all a fraud. And this is especially comforting because these same companies have for decades slandered China as capable of making only cheap junk, while hiding the real truth from consumers and the general public.
Why pay $250 or more for a t-shirt, when you can buy one for $10 made by the person sitting at the other sewing station in the sane factory.
Marketing madness.