I would say that the statement holds some level of validity. Othello's undoing is not formed from anyone outside. It is within him. Iago is perceptive enough to understand where his weakness lies in his position, his status, his love with Desdemona, and his association with others. The tragic condition within Othello is that while he has been showered with success and has earned it, there is still an level of insecurity and doubt that does not animate him to greatness, but actually drives him to question the world and his own capacity. In the end, it is the belief that individuals can be the cause of their own undoing that is present in Othello.
I'd like to comment on at least one character to support your statement. Othello's tragedy lies within his own character. This fact is evident in Act 3, Scene 3 in which Iago begins his slow manipulation of Othello's perceptions of Desdemona. He begins by using one of Othello's strengths to turn him against his wife: his faith in others. By hinting that he knows more than he is willing to tell, Iago has Othello begging him for information about Cassio and Desdemona. Othello has no reason not to trust Iago--a man whom he has placed his "absolute trust," a man who has fought alongside him in battle.
But Othello does not really fall for Iago's bait completely until Iago makes him question the credibility of Desdemona falling for someone such as he when Michael Cassio was around. He calls it "unnatural." At this point Othello looks inward,
Haply I am black
And have not those soft parts of conversation
That chamberers have, or for I am declined
Into the vale of years--yet that's not much-
She's gone, I am abused, and my relief
Must be to loathe her.
In this passage, Othello compares himself to Cassio who has the language of a courtier, is young and white, and when he does, he finds himself coming out as Cassio's inferior. So, of course, Desdemona is in love with Cassio; how could she love him. It is this conclusion that makes Othello's fall so heartbreaking and so believable. Othello falls when he looks at himself and doubts his own attractiveness to the woman he loves.
Once Othello decides that he has lost Desdemona, he moves quickly to have her and Cassio killed. In his mind, they have committed treason, and the penalty for such an act is death. He is a soldier, after all, a man of action, one who must be decisive. After a brief hearing in Desdemona's bedchambers in which Othello interrogates Desdemona of her unfaithfulness and further gathering of evidence that makes the case against her--the ocular proof--Othello moves quickly to execute her.
Othello's tragedy then stems from his own make-up. It is his sense of inferiority when he compares himself to men like Cassio that leads him to doubt Desdemona's love for him and it's his identity as a soldier that causes him to trust his ensign over his wife and take decisive action.
Unlike other tragedies that rely heavily on fate or the supernatural, Othello is a domestic tragedy in which an honorable man falls victim to a cunning villain. Its focus is on the human world, not the supernatural or unnatural. It is Shakespeare's smallest cast and most unified plot, as it has no subplots. Indeed, it is his most human tragedy.
Like the "Garden of Eden" story of original sin in Genesis, Othello also is a morality tale in which a couple is deceived by a snake in their garden. Iago, the villain of the play, knows how to bring out the worst in his victims. He uses Roderigo's lust for Desdemona against him. He preys upon Cassio's drunkenness and fixation upon reputation, and--of course--he exposes Othello's rage, jealousy, and sense of inferiority in terms of his race, religion, age, and rank. And let us not forget the women: Desdemona and Emilia, both are killed by their husbands, both innocent victims of sexism.
The play is Shakespeare's most Aristotelian. After Act I, it has unity of place, action, and time as it is confined to a remote island with a sparse cast, no subplot, and a rapid fall of its hero.