My understanding is that this was a judgment call. It had been in the Old Latin texts, and so the question was: How did it get there so early and where would it have come from?
Since the Old Latin had been originally translated from the Greek vulgate beginning around 150 AD, it was thought to have been in the Greek vulgate at that time. Then about 70 years later when the Sabellian heresy was plaguing the East around 220 AD, it was believed to have been removed from the text to quell the heresy, since this verse was often quoted by Sabellians as their proof text. But since the Sabellian heresy was not as pronounced in the West, it survived in the Old Latin bibles.
It is cited by Tertullian, Cyprian, Augustine, and Jerome. Though Jerome did not put it in his Latin Vulgate, but it was put into the Vulgate around 800 AD from the Old Latin. It was included in Erasmus' 2nd edition and subsequent bibles including the KJV because of its long useage in the Latin-speaking church --- not deception or fraud or forgery, but tradition and a judgment call.
I don't believe Erasmus had any sinister motives; tradition and honest (mis)judgment — yes.
Unfortunately, his good intentions resulted in errors which were then multiplied across the Latin-speaking world, as you said.
The idea is not to condmen his good intentions, his honest work, but the unfortunate result of it, correct it as best as we can and move on. KJV sould be retired for all those reasons resulting in unintentional errors.
Scholars today prefer the Alexandrian-type text for obvious reasons.
Excellent post!