Good question. The object sitting on the record is moving in a circle. Now pretend that the record does not exist, but instead, some arbitrary force holds the object in a circular path. You know that this force must be the centripetal force because if it were not, the object would go off on a path tangent to the circle. This arbitrary force is the friction of the record. Now the reaction force is actually the friction from the object acting on the record, but this force is not great enough to alter the record and is therefore negligible.