I have not previously seen this distinction in this context. I asked American Express about this by Chat, and was told that Supplementary Platinum cardholders can enter Centurion lounges, but cannot bring guests. The agent was unable to show me where this policy is written, other than to assert that any portion of the lounge rules that mentions guests refers to the basic (primary) cardholder.

I believe a family of four with one supplementary Platinum card should still be OK. Primary cardholder admits self and two children as guests. Supplementary cardholder admits self.

However, I am not persuaded this interpretation was intended when the rules were published, nor that it has been enforced in practice. Of course this may change, and we'll see what is reported over the summer family travel season.