THEY REQUESTED NO SERVICE
There are many reasons why a person
might say they don't want a service.
Most of the time it is because they don't want to burden someone else.
The one thing to remember is that services are to help the ones that are left after a death find peace, comfort, and closure. It is important to honor the wishes of the deceased, but it is also important to take care of the wishes of the family as well.
If you feel that having a service will help you and your family heal, then by all means hold one.