"from Greek barbaros 'foreign, strange, ignorant,' from PIE root *barbar- echoic of unintelligible speech of foreigners (compare Sanskrit barbara- 'stammering,' also 'non-Aryan,' Latin balbus 'stammering,' Czech blblati 'to stammer')." I don't know if the source I'm quoting is reliable, but I find the same reference to Sanskrit in a variety of sources.
Interesting. Though I knew Sanskrit (well in school), didn't know or remember that word - but still know Hindi well, and in Hindi, bad-bad (pronounced like bud-bud) means blabbing, as in:
Kya bad-bad kar rahe ho - What are you blabbing.
And to close the loop, in Hindi, the sounds r and d are closely related and sometimes substituted for one another - at least while talking.
Pretty sure this explanation is just really old speculation. Even if the ancient greeks kept records of word origins, those documents would likely be lost by now
Judging by this link: http://www.etymonline.com/index.php?term=barbarian,
the reasoning is based on words in other indoeuropean languages having a similar root to 'barbarian' being used to refer to stammering or incoherent speech.