You have neglected to impart one very vital piece of information here.

How many checked bags did your party check in, prior to requesting that "hand baggage" also be checked?

A "hand baggage" allowance only applies to luggage that you carry with you into the cabin. You cannot arbitrarily decide to check in your "hand baggage" allowance for free if you have already used up your allotted checked luggage allowance.

As soon as you check in an item, it stops being "hand luggage", and becomes regular checked luggage. You cannot add your hand luggage allowance to your existing checked luggage allowance, and expect the total to all be checked for free.