It's not just today's media that reports on scandalous stories of foreign decadence that probably aren't true. In 1912 the New York Times reported that Parisian women were injecting perfume into themselves. Sounds like a good idea to me.
For about twenty years, from the late 1800s to the early 1900s, papers all over America periodically ran articles about how French women injected perfume under their skin. This was at a time when perfume was coming down in price and the middle class was growing. Many people, not only women, used scent, and there were detailed guides on what scent to use, when to use it, and where to apply the scent. (Some of the guides gave dire warnings. Certain scents were supposed to be intoxicating or sickening, especially to vulnerable young women.)
Today we take it for granted that perfume is applied to the skin. In late Victorian period, this was improper. Women applied scent to their handkerchiefs and their clothes, not to their bodies. This might be because a little scent wouldn't make it through their layers of clothing. And, of course, only one "kind of woman" would need to be scented even when her clothes were off.
Injecting perfume, then, was both decadent and scandalous. It was probably cobbled together from a number of different stories — women using too much perfume, people drinking a little perfume as a show of wealth, and women injecting other things subcutaneously. While I'm not eager to shoot up a perfume, there was a seed of a good idea here.
We're constantly bombarded with deodorant ads, mouthwash ads, and scented lotion ads. Reports of perfume injection state that the women "exhaled" the fragrance and that it emanated from their skin. Perfuming your saliva might get in the way of enjoying food, but finding a way to perfume sweat sounds like it could make someone a fortune.
If people are willing to dab things on their eyes every day to grow their eye-lashes longer, and inject botulism into their faces to stave off wrinkles, surely a pill or a shot that makes your sweat smell like orange blossom would be worth some research.