http://www.lds.org/manual/preach-my-gospel-a-guide-to-missionary-service/how-do-i-prepare-people-for-baptism-and-confirmation?lang=engWho conducts the interview for baptism?
Normally the district leader interviews baptismal candidates taught by missionaries in his district, including candidates taught by his zone leaders. The zone leader interviews candidates taught by the district leader. The mission president or someone he assigns must interview people involved in serious sins. District or zone leaders do not interview baptismal candidates outside their own district or zone unless the mission president assigns them to do so.
What is the definition of a convert baptism?
Convert baptisms are baptisms of:
•Persons ages nine and older who have never before been baptized and confirmed as members of the Church.
•Children age eight whose parents are both nonmembers or whose parents are being baptized and confirmed at the same time as the child.
Do I need permission to baptize a minor child?
Before you can teach and baptize an investigator who is under legal age, you must obtain permission of the parent(s) or legal guardian(s), preferably in writing. In addition, you should have good reason to believe that the child understands the baptismal covenant and will make every effort to keep it through obedience to the gospel, including faithfully attending Church meetings.
Do I need permission of the spouse in order to baptize a husband or wife?
Yes. Do not baptize a married person without the consent of his or her spouse.
In the situation above with the mentally challenged 13 year old. Their parents probably did consent, thinking it might be helpful either to the child to have a group of friends, or perhaps they might even have wanted the potential support. Doesn't matter as that's not the point. In actual fact, depending on the level of their mental faculty, it was perhaps not only inappropriate, but unnecessary.
The Church of Jesus Christ of Latter-day Saints General Handbook of Instructions given to the priesthood leaders gives the following information concerning persons who are not accountable. “Persons who are not accountable and cannot knowingly repent need not be baptized, no matter what their age. They should be included as members of record with the notation ‘Not accountable’ recorded under the heading for baptism. If they become accountable, they can then be baptized.” (1968, p. 85.)
http://www.lds.org/ensign/1976/04/i-have-a-question?lang=engMental retardation includes a large range of abilities and disabilities from almost normal to completely incapacitated. Many mentally retarded persons are above the mental level of eight years, and as the General Handbook of Instructions directs, if such persons become accountable “they can then be baptized.” Other, more severely retarded, children will never be accountable. It is the responsibility of those who are appointed “Judges in Israel” to make inspired decisions concerning accountability. When this judgment is made, parents should feel assured that the Lord will give the retarded person every opportunity and blessing promised to the faithful.
How did the missionaries and person conducting the interview for baptism assess the mental age of the 13 year old child?