The accuracy of an individual's discharge certificate depends on a number of factors. As for "the whole truth", there are only so many blanks on the form and only so much space in each blank. The discharge certificate is a brief summary of an individual's active service and, for obvious reasons, doesn't include information beyond the individual's date of separation.
What is the "whole truth" you're seeking? A number of "task forces" existed during World War II. Which one is of particular interest?