The sign/kiss of peace is found in the General Instruction of the Roman Missal. It is used throughout the world. It is, however, optional.
The sign/kiss of peace was part of the earliest Christian liturgies. Numerous ancient liturgical texts make reference to it (Justin Martyr is the first). Over the centuries this part of the Mass took on various forms and eventually was only shared by the clergy. It remained this way from the Council of Trent until the liturgical reforms of the Second Vatican Council.
Your friend is incorrect that the sign/kiss of peace is not in the "original rite" of the Mass.