Hi Neil, I believe that message means that the Hubspot user seat attempting to set things up lacks sufficient permissions to do so. A HS Super Admin would, though.
As for exactly what the Clay/HS integration would need, I believe this would cover it:
crm.lists.read
crm.objects.companies.read
crm.objects.companies.write
crm.objects.contacts.read
crm.objects.contacts.write
crm.objects.deals.read
crm.objects.deals.write
crm.objects.owners.read
crm.schemas.companies.read
crm.schemas.contacts.read
crm.schemas.deals.read