Really they can’t claim older rite? from Catholic encyclopedia
The most explicit passage is in the letter of Pope Innocent I to Decentius: "As regards the sealing of infants, it is clear that it is not lawful for it to be done by anyone but a bishop [non ab aliis quam ab episcopo fieri licere].
Thus the Synod of Worcester (1240) decreed that parents who neglected to have their child confirmed within a year after birth should be forbidden to enter the church. The Synod of Exeter (1287) enacted that children should be confirmed within three years from birth, otherwise the parents were to fast on bread and water until they complied with the **law. **
clearly baptism, chrismation and first communion given together even to infants is the oldest tradition in the church.