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I was told the very same thing as an elementary school student by Sisters of Mercy in 1957. That experience, coupled with the imprimatur, tell me that this was the belief of the Latin Church

Well, given that the Catholic Church did nothing to stop forced mass conversions of Orthodox Serbs in fascist puppet-state of Croatia (1941-1945), one is led to believe that this was indeed the teaching of the Catholic Church. I would like to think otherwise, but for the imprimatur to make such an oversight just seems a little too naïve.

By the way, Petrosius, what was the official teaching of the Catholic Church vis-a-vis the Eastern Orthodox Church in the 1930's?

When a bishop who has fallen into heresy is reconciled he is not reconsecrated. Therefore he did not lose the power which he had of conferring Orders. Furthermore, the power to ordain is greater than the power of Orders. But the power of Orders is not forfeited on account of heresy and the like. Neither therefore is the power to ordain. Further, as the one who baptizes exercises a merely outward ministry, so does one who ordains, while God works inwardly. But one who is cut off from the Church by no means loses the power to baptize. Neither therefore does he lose the power to ordain.
--St. Thomas Aquinas, Summa Theologica, Suppl. 38, 2.

Those ordained by schismatic bishops, who have been otherwise duly ordained, the due form having been observed, receive, indeed, ordination, but not jurisdiction.
--Pope Clement VIII, Instruction concerning the rites of the Italo-Greeks (1595), D1087.

Can. 2372. He who presumes to receive orders from one excommunicated or suspended or interdicted after a declaratory or condemnatory sentence, or from a notorious apostate, heretic, or schismatic, ipso facto contracts a suspension a divinis, reserved to the Apostolic See; however he who should be ordained in good faith by any of them lacks the exercise of the order so received until he shall be dispensed.
--Code of Canon Law (1917).
[Note: The implication is that such ordinations are valid.]

Every validly consecrated bishop, including heretical, schismatic, simonistic or excommunicated bishops, can validly dispense the Sacrament of Order, provided that he has the requisite intention, and follows the essential external rite (sent. cert.).
--Ludwig Ott, Fundamentals of Catholic Dogma (1955), p. 458.