As far as I know - there is no such thing as a no-kill shelter. Like in this case - these dogs were moved to a shelter to be put down.
And - for any reason - once you give your pets away to a shelter, you no longer have any right to question what becomes of them.
You’re right, there really are not any no kill shelters. The ones that claim to be actually fudge their numbers by euthanizing before they ‘count’.