Speaking at the Royal United Services Institute last week, Dearlove, who headed MI6 from 1999 to 2004, emphasised the significance of Prince Bandar's words, saying that they constituted "a chilling comment that I remember very well indeed".
He does not doubt that substantial and sustained funding from private donors in Saudi Arabia and Qatar, to which the authorities may have turned a blind eye, has played a central role in the Isis surge into Sunni areas of Iraq.
"The Shia in general are getting very frightened after what happened in northern Iraq," said an Iraqi commentator, who did not want his name published.
Shia see the threat as not only military but stemming from the expanded influence over mainstream Sunni Islam of Wahhabism, the puritanical and intolerant version of Islam espoused by Saudi Arabia that condemns Shia and other Islamic sects as non-Muslim apostates and polytheists.
Coverage of Dearlove's speech focused instead on his main theme that the threat from Isis to the West is being exaggerated because, unlike Bin Laden's al-Qa'ida, it is absorbed in a new conflict that "is essentially Muslim on Muslim".