This statement is false. Gregory the Great condemned the title universal bishop in the sense of meaning that all other bishops are not really bishops, but mere agents of the one Bishop, a concept that is blatantly contrary to Catholic teaching, which holds that all bishops are by divine institution true successors of the Apostles. For he states:
For if one, as he supposes, is universal bishop, it remains that you are not bishops.
Gregory clearly upholds the universal authority and supremacy of the Roman bishop as stated in his Epistle XLIII,
To all who know the Gospel it is clear that by the words of our Lord the care of the whole Church was committed to Blessed Peter, the Prince of the Apostles . . . Behold, he received the keys of the kingdom of heaven, the power to bind and loose was given to him, and the care and principality of the entire church was committed to him