Ascribing a quotation to a great man without naming him
If the critical distinguishing feature of the formulation "A great man once said [or wrote]" is the ascribing of an actual quotation—and not merely an aphorism—to an unnamed "great man," perhaps an instance from Montaigne's 1588 essay "De l'Art de Conferer" ("Of the Art of Conferring [or Conference]" in earlier translations; "Of the Art of Discussion" in Donald M. Frame's translation) qualifies, though Montaigne may have expected his readers to recognize the quotation and to know that its author was Quintus Curtius:
Ce qu'il [Tacitus] dict aussi que Vespasian, par la faveur du Dieu Serapis, guarit en Alexandrie une femme aveugle en luy oignant les yeux de sa salive, et je ne sçay quel autre miracle, il le faict par l'exemple et devoir de tous bons historiens: ils tiennent registre des evenements d'importance; parmy les accidens publics sont aussi les bruits et opinions populaires. C'est leur rolle de reciter les communes creances, non pas de les regler. Cette part touche les Theologiens et les philosophes directeurs des consciences. Pourtant tres-sagement, ce sien compaignon et grand homme comme luy: Equidem plura transcribo quam credo: nam nec affirmare sustineo, de quibus dubito, nec subducere quae accepi;
From the John Florio translation (1603):
Where he [Tacitus] also saith that Vespasian, by the favour of the God Serapis, healed in the citie of Alexandria a blinde woman with the rubbing and anointing her eyes with fasting spettle, and some other miracles, which I remember not well now, he doth it by the example and devoire of all good historians. They keepe a register of important events; among publike accidents are allso popular reports and opinions. It is their part to relate common conceits, but not to sway them. This part belongeth to Divines and Philosophers, directors of consciences. Therefore, that companion of his, and as great a man as hee, said most wisely: Equidem plura transcribo quam credo: Nam nec affirmare sustineo de quibus dubito nec sub ducere quæ accepi: 'I write out more then I beleeve: for neither can I bide to affirm what I doubt of, nor to withdrawe what I have heard.'
From the translation by Charles Cotton (in an edition published in 1877):
What also he [Tacitus] says, that Vespasian, "by the favour of the god Serapis, cured a blind woman at Alexandria by anointing her eyes with his spittle, and I know not what other miracle," he says by the example and duty of all his good historians. They record all events of importance; and amongst public incidents are the popular rumours and opinions. 'Tis their part to relate common beliefs, not to regulate them: that part concerns divines and philosophers, directors of consciences; and therefore it was that this companion of his, and a great man like himself, very wisely said: "Equidem plura transcribo, quam credo: nam nec affirmare sustineo, de quibus dubito, nec subducere quae accepi;"
Montaigne never cites Quintus Curtius by name in this essay or in any other; a scholarly work ("List of Some Authors Read by Montaigne" in Grace Norton, Studies in Montaigne (1904), page 279) asserts that Montaigne quotes Quintus Curtius seven times in the course of his Essays without attribution.
Early occurrences of 'a great man once said'
On a more literal level, the exact phrase "a great man once said" appears in at least two sermons of the eighteenth century. From the "Sermon, II' in Increase Mather, Wo to Drunkards. Two Sermons Testifying Against the Sin of Drunkenness, second edition (1712):
Know for certain, that who ever liveth & dieth in this Sin, shall Perish to Eternity. It will be a folly for any such Sinner to expect Salvation. Can you be Saved without an Interest in Christ? This Lust alone, if lov'd or liv'd in, will keep Christ out of the Soul. It is reported, that a great man once said to Luther, Sir, we would all willingly be Christians, but we cannot find in our hearts to leave that custom of drinking to Excess. But a man must leave that Custom, or Die & Perish a Christless Sinner for ever.
Here, it should be noted, "a great man" probably means "a man of substance or importance in the world," not "a man of literary, artistic, or philosophical genius."
And from James Burgess, "Beelzebub Driving and Drowning His Hogs. A Sermon on Mark V. 12, 13" (1770):
And now, sinners, bethink yourself seriously, whether it be not the height of folly to permit yourselves to be driven by the evil spirit and your own lusts down the fatal precipice of vice, and to wallow in those brutal gratifications which will render you contemptible here, and miserable hereafter. As a great man once said, "Words cannot fully describe the madness of those sinners, who, that they may live the life of beasts here, stick not to share the lot of devils hereafter." What a pity is it that sinners do not lay these awful considerations to heart!
Here the "great man" is presumably a great theologian—though not one that Burgess chooses to name.
But there is also this secular occurrence of the related phrase "a great man once told me", in a 1736 translation of The Dictionary Historical and Critical of Mr. Peter Bayle
Early occurrences of 'a wise man once said'
Closely related to the expression "a great man once said"—but evidently somewhat older—is the expression "a wise man once said." I found three instances of this expression in books by English writers (not translators) from the seventeenth century.
From Henry Parker, The Trojan Horse of the Presbyteriall Government Vnbowelled (1646):
Men grossely ignorant in matters of Divinity, must be Judges of Doctrine; and they that cannot in a small time be taught what heresie is, much lesse how to discern heresie from truth, determine of it, and others be bound to submit to their judgement. Men whose education and imployment is either in the field, or the shop, of whom a wise man once said, that they should not be sought for in publique councell nor sit on the judges seat, because they understand not the sentence of Judgement; men who neither know how to doe right if they would, nor would care for it if they knew it, (for where the minde that should rule is weake, the corrupt passions that should be ruled, breake out into all disorder:) These must be trusted with the making of church-Lawes, and Government even of those things that concern the precious souls of men for whom Christ died; to say nothing of their quiet, their reputation, and their purses, which will be all exposed to those injuries that may be expected from blind malice, revenge, envy, covetousnesse, partiality, and insolence. All these mischiefs are the more to be feared, in regard of the distempers of this sad time, in which this Government is sought to be erected.
From Symon Patrick, The Parable of the Pilgrim: Written to a Friend (1667):
But whatsoever kindness any may have for them [people of "sullen gravities" and "lowring Countenances"], I must acknowledge myself to have a Spirit more tender. I am not ashamed to be thought a man of sense, and that have some feeling both of pain and of pleasure. Let them call, if they list, all our passions infirmities, yet (as a wise man once said) I rather choose to enjoy this weakness, then their stoutness and strength, and to be sick of this disease, then to have their kind of health.
And from Symon Patrick (again), The Heart's Ease, Or, A Remedy Against All Troubles, seventh edition (1699):
We multiply our evils by our trouble, and bring those upon our selves which perhaps were never intended for our portion. But our quietness disappoints the Enemy, and will weary him in his assaults, when he sees that we do but grow better by what befals us, and turn it into vićtory and triumph. So a wise man once said, No man ever reproached me more than once ; for by patient bearing his reproaches the first time, I taught him to abstain the second.
Patrick was Bishop of Ely in the Church of England from 1691 to 1707.
Conclusion
For centuries, people have used the literary device of citing an authority as "great" or "wise" without identifying the person by name. The earliest instance I've found of the exact wording "a great man once said" is from a sermon against drunkenness by Increase Mather, published in 1712. The earliest instance I've found of the related expression "a wise man once said" is from a 1646 polemic against Presbyterianism by Henry Parker.
Best Answer
Your teacher has limited experience. "It is no secret that ..." tells me clearly "It is well known that ..." or "It is common knowledge that ..." The construct is not in the least obscure, nor is it in any way informal. I encourage you to use it freely.