I may have misread his reply, but I took the information after the "insofar" to be referring to the Chalcedonians' rejection of iconoclasm, not a claim that they only accept the first three councils.
Quite right - that was exactly my point!
My overall point is that of the seven ecumenical councils held in common between the Eastern Orthodox and Roman Catholics, while the Oriental Orthodox only participated in the first four, and only recognize the first three councils, when it comes to the theology of the subsequent councils, the specific heresies that they were intended to anathematize, that is to say Eutychianism*, Monergism, Monothelitism and Iconoclasm, have always been rejected by the Oriental Orthodox as well. Indeed Eutyches was anathematized by Pope Dioscorus before the Council of Chalcedon - I really feel that he should not have been deposed.
The Oriental Orthodox subsequently suffered greatly, especially after Emperor Justinian, for unknown reasons, stopped pursuing a policy of reconciliation with them and instead began a violent persecution, and switched from embracing Theopaschitism to Apthartodocetism - fortunately his incorporation of the hymn Ho Monogenes (“Only Begotten Son and Word of God”) into the Byzantine Rite liturgy, a hymn originally written by Mor Severus of Antioch, remained. Later, on several occasions, the Oriental Orthodox were falsely accused of Monophysitism, but the Monophysites were in fact a distinct sect, which degenerated into Tritheism. It did not help with this confusion that the Monophysites largely resided in Egypt, but they were predominantly Greek speaking - the last Monophysite leader of note was the Tritheist philosopher John Philoponus.
Actual Monophysitism leads inevitably to Tritheism, because it is incompatible with the Nicene doctrine of the Consubstantiality of the Son with the Father, and with Humanity. By making Our Lord out to be a sort of hybrid, with His humanity blasphemously asserted by Eutyches to have been dissolved into His divinity “like a drop of water into the ocean”, He would be, in such a case, not consubstantial with the Father, and as such the only way to avoid Arianism would be to worship the three persons of the Holy Trinity as three separate gods. Thus the modern day successors of Eutyches are in fact the Mormons, although they are unaware of this, and also don’t care, since they reject the Nicene Creed and believe, like most other Restorationist sects, that there was a Great Apostasy after the last Apostle died, Matthew 16:18 not withstanding, until some random 16th-19th century prophet came along to set things right (controversially, I classify certain churches of the Radical Reformation and related movements that also believe in a Great Apostasy, for example, some Quakers, and also the Shakers, and anyone else who claimed to be restoring from non-existent the Early Church as Restorationist).
Likewise the Oriental Orthodox reject Monergism, embracing a Synergistic model of soteriology closely related to the Eastern Orthodox model, since the whole idea of Theosis is most eloquently expressed in St. Athanasius, On The Incarnation.
And in all probability, the schism that resulted in the Maronites leaving the Syriac Orthodox and establishing their own church in the hills of Lebanon was over Monothelitism. Aside from the evidence of Monothelite belief many Catholic scholars found (which left liturgical traces, which were suppressed in the years after the Maronites established a formal permanent communion with Rome during the First Crusade), this also explains why the Maronites were favorably inclined to the Roman Catholics to begin with, since, in addition to the high Petrology which characterizes the Syriac Orthodox Church, the Maronites also would likely have been aware at the time of their schism from the Syriac Orthodox that Pope Honorius I was among the more active promoters of Monothelitism (which led to him being anathematized at the Sixth Ecumenical Synod - he is the only legitimate Bishop of Rome, with the exception of some antipopes, to be anathematized by one of the first seven Ecumenical councils).