Incorrect. If that were the case, the gates of Hell would have prevailed against the Church over a thousand years ago when Honorius gave tacit approval to the Monothelite heresy. Remember: Honorius was *anathematized* by an ecumenical council, and I believe that anathema carried Pope Agatho's approval.
The Pope can commit heresy personally. He just can't define it ex cathedra as binding on the whole Church. Read the definition from Vatican I very carefully and note what it says and doesn't say. The Fathers at that council had the case of Honorius staring them right in the face when they made the definition.
The Pope can commit heresy personally. He just can’t define it ex cathedra as binding on the whole Church.
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Please consider this quote in rebuttal to your above claim:
The question was also raised by a Cardinal, “What is to be done with the Pope if he becomes a heretic?” It was answered that there has never been such a case; the Council of Bishops could depose him for heresy, for from the moment he becomes a heretic he is not the head or even a member of the Church. The Church would not be, for a moment, obliged to listen to him when he begins to teach a doctrine the Church knows to be a false doctrine, and he would cease to be Pope, being deposed by God Himself.
If the Pope, for instance, were to say that the belief in God is false, you would not be obliged to believe him, or if he were to deny the rest of the creed, “I believe in Christ,” etc. The supposition is injurious to the Holy Father in the very idea, but serves to show you the fullness with which the subject has been considered and the ample thought given to every possibility. If he denies any dogma of the Church held by every true believer, he is no more Pope than either you or I; and so in this respect the dogma of infallibility amounts to nothing as an article of temporal government or cover for heresy.
(Abp. John B. Purcell, quoted in Rev. James J. McGovern, Life and Life Work of Pope Leo XIII [Chicago, IL: Allied Printing, 1903], p. 241)
(From: http://novusordowatch.org/2015/04/vatican-i-popes-follow-up/)