It is true in a sense, but now it depends how much exaggeration one side will take it or how they would interpret it to mean.
Constantine the Great (thus the alias I have) started a line of Holy Roman Emperors where secular rulers worked hand in hand with the Church. Think “New Testament King David”. They have the power to summon bishops to a council because they are the secular ruler. Because of the ecclesiology of the First Millennium, no one bishop had the authority to summon all the bishops of the empire. The emperor, being a temporal ruler, had that authority. It helped stem the issue whether one bishop had authority to summon another, especially if these were two Metropolitans. Patriarchates were just beginning to come into order at this time.
The Emperor has the perogative to choose who can become bishop, but the Church was not beholden to it. Usually it is part of the politics between Church and state. But the emperor surely did not choose bishops for the entire empire, nor is his choice final. The other bishops can surely refuse, but then they have to face the possible strain in relationship.
Remember when there were 3 claimants to the Papacy in Rome, the Emperor helped sort that out.