You're right to be skeptical of the connection. I wrote on this topic before, and touched on the specific story, so I'll repost that here.

Piercings, generally, go back many millennia, with references to be found in some of our earliest literature, such as the book of Genesis, which makes reference to earrings, and piercings of sexual organs are fairly ancient as well. Some of the earliest textual references to piercings of the gentalia come to us from Roman writers, who make reference to male infibulation, that is, foreskin piercings. It seems to have been done at least in some cases for medical reasons, at least based on the earliest reference by Aulus Cornelius Celsus who describes the procedure in the early 1st century. Writing shortly after him, and giving us support for a sexual function, the satirists Martial and Juvenal make many references to penile 'pins' and imply that performers, especially comedians, would wear them to "enhance their sexual attractiveness". It seems that for the most part though, they were worn as Penis Jewelry, and taken off for the sex act, as there is, for instance reference that "Some pay a lot to undo the pin of a comic actor", implying the removal of the pin after catching the eye.

Not all piercing were meant for removal though, and nearly contemporary to these Roman writers another, quite explicit (as you might expect) description comes from the Kama Sutra, which makes mention of a penile piercing as a sexual enhancement device:

The people of the southern countries think that true sexual pleasure cannot be obtained without perforating the Lingam [penis], and they therefore cause it to be pierced like the lobes of the ears of an infant pierced for earrings.

It seems that this was already an established practice by the time the book was written sometime between the 1st and 6th centuries, based on the manner in which it was mentioned. The text isn't entirely clear on where the piercing was done, but it is surmised to likely have been through the foreskin.

Going further back, artifacts recovered from various European sites dated to the Upper Paleolithic (38,000 to 11,000 years) show evidence not only of piercings, but also tattoos and scarification of the 'male member', but we of course lack written records to explain precisely how such practices were viewed or how widespread they were outside of art.

In more recent centuries, there is evidence of some pre-20th century piercings, such as claims about nipple piercings mentioned in Victorian era literature (see here for discussion of the veracity), but on the whole many supposed histories of genital piercings are rather mythic, and trace their origins to the rise of interest in the latter half of the 20th centuries, pioneered by piercers and jewelry artists such as "Mr Sebastian", Fakir Musafar, Jim Ward, and Doug Malloy. Looking to add glamour and mystique they took to concocting stories to give various piercings 'history', such as Prince Albert requiring a "Prince Albert" to prevent an overly obvious bulge, or Roman Centurions having nipple piercings which they attached their short capes to.

Renaissance writers, remarking on the Roman references such as those mentioned above, were generally critical, and there is little to suggest they themselves approved of the practice, although they do leave us reports of encountering various practices encountered in other lands, but are of often dubious veracity. Writing in the 18th century, Cornelius de Pauw remarked for instance:

Also the Caloyers or Greek monks, who perform acts of penitence almost as bizarre as the Fakirs and the Bonses, have themselves infibulated with the largest ring a man can tolerate. Among these frenzied creatures, one meets those who wear in their foreskin a ring of iron, six inches in circumference, weighing more than a quarter of a pound. It is impossible to imagine a form of fanaticism more cruel than this. Perfect resignation and superhuman patience is necessary to tolerate these fetters, which proves how difficult it would be for these celibate Asiatics to maintain their vow of chastity if they did not take care to tie themselves up. One also reads of similar things among Turkish monks, such as the Calenders, Dervishes, and the Santons, who also wear these muzzles, and whose holiness the people judge according to the largeness of their rosary and ring. This is all the more astonishing because these miserable creatures are circumcised. They apparently unfasten these rings when they commit the enormous crime of which they are accused. To mortify their flesh and their minds, they occasionally couple with mules and she-asses, while the mule driver, devotedly kneeling, thanks these saints for the honour they do to his animals.

Certainly, some of the reports were likely true, or based on the truth, as we have ample evidence for the practice by various non-western groups, but regardless, the western reports from that period mostly focus on its exoticism, and such writings, no matter the topic, have a tendency for the grandiose.

Now of course, there was a resurgence of male infibulation in the 19th century Western World, but it was for anything but sexual pleasure. Carl August Weinhold proposed using it as a method of population control and eugenics, a male chastity belt of sorts, to be placed by the state on any person deemed unfit to have children, such as criminals or the mentally ill. More infamously, it was extensively pushed as an anti-masturbatory device to prevent what was seen as a terrible disease, and was only abandoned in the early 20th century.

As previously mentioned, we see the resurgence of genital piercings in the Western World in the latter half of the 20th century, and once again of a sexual nature. I will, of course, note that I've really only focused on male piercings here, rather than female, which opens itself to a whole new answer, and which I will leave to someone else.

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Sources:

Anderson, W. R., Summerton, D. J., Sharma, D. M. and Holmes, S. A. (2011), A guide to genital piercing. Trends in Urology & Men's Health, 2: 31–36.

Angulo, Javier C. (12/01/2011). Phallic Decoration in Paleolithic Art: Genital Scarification, Piercing and Tattoos. The Journal of urology. , 186 (6), p. 2498 - 2503

Ferguson, H. (1999). Body piercing. BMJ : British Medical Journal, 319(7225), 1627–1629.

Schultheiss, D., Mattelaer, J.J. and Hodges, F.M. (2003), Preputial infibulation: from ancient medicine to modern genital piercing. BJU International, 92: 758–763