That is only for the student not spouse or children. As I said before the airline will be determining whether they feel your travel is non-discretionary. It is unclear how each airline determine whether travel is non-discretionary and whether they will just let any spouse accompany or not.
"If immediate family members want to be with you in Canada
Your immediate family members may be able to come with you to Canada.
If they travel with you
They don’t need a written authorization from IRCC to travel with you. However, they must show that their reasons for travel are non-discretionary (non-optional). For example, they’ll help you get established and support you in Canada"
You seems to be right as what they updated on their official website but they replied me with the following different aspect of that.
Immediate family members of international students won't need written authorization if they plan to travel with the international student. You can find more information on that process here, see "If they travel with you": https://canada.ca/en/immigration-refugees-citizenship/services/coronavirus-covid19/students.html#travel….