Great find. At the bottom of the page you linked, there is a link to the data for private schools in Ca:
https://www.cde.ca.gov/ds/si/ps/ You can find Sandcastle Day School in the data for 2014, 2015, and 2016. Even though they were a school as of 2011, they must not have had 6 students "enrolled" because you have to have 6 students to be in the database.
Point to note: They listed themselves as NOT a religious school.
ETA:
In 2014-15, they had students enrolled in grades 3,4, 6, 7. 8. 10, 11, 12 (8 kids)
In 2015-16 all bumped up a grade, with kids in grades 4, 5, 7, 8, 9, 11, 12 (7 kids)
In 2016-17, all bumped up a grade, with kids in grades 5, 6, 8, 9, 10, 12 (6 kids)
I do not understand why their data for prior years isn't in the databases. They would have had even more kids in school then.
However, this data DOES support the notion that there were only 6 kids and 7 adult children in the house. After last school year, there would have been only 5 kids still in school.
Note: What on EARTH were those 7 adult children doing all day every day?