The Consilium clarifies the level at which liturgy may be … tampered.
45. Especially in the celebration of the eucharist, only the supreme authority of the Church and, according to the norm of law, the bishops and the conferences of bishops, no one else, not even a priest, may, on his own initiative add, leave out, or change anything in the liturgy. [See Sacrosanctum Concilium art. 22.] Therefore, priests should be intent on presiding over the celebration of the eucharist in such a way that the faithful know that they are participating not in a rite decided on by private authority, [See Summa Theologiae 2a2ae, 93,1.] but in the public worship of the Church, the direction of which has been entrusted by Christ to the apostles and their successors.
Vatican II removed the sole authority for liturgical changes from the “supreme authority,” and within church law, places some of it with conferences and individual bishops. Why is it important for “even a priest” not to alter the liturgy? Because of the need for worship from a public authority.
Some Catholics are quick to hop on this as a club against clergy and others who take legitimate options provided in the rites. A priest may lawfully leave out the Penitential Rite, for example, on some occasions. But the Sign of Peace cannot lawfully be omitted.