Yeah, they might have stretched it too far.
(1) The Greek text of "Barlaam and Josaphat" - composed by the learned monk St. John Damascene - consists, in large part, of Josaphat and Barlaam arguing in favor of Christianity to King Abenner.
The speeches of these two are basically a verbatim transcription of the Apologion of Aristides, a Greek Christian who argued on behalf of Christianity to Emperor Hadrian in 126. This discovery has been common scholarly knowledge for a century.
(2) Therefore, some suspect that "Barlaam and Josaphat" was written by the Damascene as a conscious literary ploy, creating a text meant to be used to missionize Buddhists.
This makes sense, since it uses the tropes of the life of the Buddha to point to someone higher - Christ.
The argument is made that if the story originally came from Buddhists and was not deliberately constructed by the Damascene, why would the Buddha figure be portrayed as subordinate to Christ?
One thing is certain - the Josaphat story as it was known in the Middle Ages is traceable entirely to the Damascene's text.
We do not know where he got the idea to transform Aristides' Apologion into a hagiographical narrative, but we know exactly where medieval Christians got the story.