You know, I know several home educated children who spend all of their time with their parents. All. Of. Their Time. Where grandparents and friends are very welcome to join the family, but one or other parent will still be in the vicinity.
IME, there is always a very good reason for it, usually involving a special need of some kind, even if that special need is never openly discussed. And it's often an extension of an AP-stylee beginning for those who find themselves with a child on the autistic spectrum, whose needs are very challenging, and who cannot easily express themselves to other people. The parents are very tuned in, and that's the only way they keep things smooth.
Of the families in that situation that I know personally, there are often one or more siblings who the parents wave off for days/weekends away with other people without a backward glance.
I know other families where a neurotypical child has had a bad nursery or school experience which takes them months or even years to recver from, with total screaming abdabs at the idea of separation from primary carers. Taking the child out of that situation was a point of no return for the family, who are working long term to regain the child's trust and build up their confidence.
You haven't mentioned what the parents were planning to do for childcare with the other children, but your OP does make me wonder whether this is one of those situations, in which case I'd advise to you take your judgeypants off and try walking a mile in that family's shoes before assuming that failure to feel comfortable with using non-family caregivers is a matter of overprotection rather than of responding appropriately to a child's developmental needs. Of course, I may be totally wrong, and these parents may be the king and queen of smother. But I'd want to give them benefit of doubt if poss.