It may seem a little strange, but QC uses ''list entities'' that are stored separately to the ''field'' entities. The field is associated with a given list, and the list appears in a drop-down in the GUI when working with the Defect. It is common practice of using QC's Workflow/scripting logic in the GUI to swap out the lists to provide context-sensitive lists. For instance effectively ''hiding'' various possible values from the user when they do not make any sense.
Usually when working with any synchronizing or API (advanced programming interface) record population (as ALM Synchronizer does), it is recommended to create and use a list that is a superset of all of the possible ''Resolution'' list values and make that the ''default'' list (the one associated with the ''Resolution'' entity from the ''Customize'' menu). Then add logic to the GUI behavior to handle Status = ''New'' and set the appropriate short list to ''Resolution'' (on the fly) instead of using the short list as the default.
The API will see the ''default'' list and will be able to set any value -- this assumes that the values being sent from the corresponding Issue in JIRA have ''legal'' value combinations in the various fields as well.