I don't know if the story's true or not, but carrying anthrax in an envelope wouldn't prove or disprove its authenticity.
True, it would expose the person carrying it to anthrax, but it may take a week or more to actually debilitate the carrier, by which time he could be expected to infect many. Considering how the Iraqi regime has total disregard for its troops' life or safety, it wouldn't be inconsistent for them to use them this way. An uneducated peasant might not even know that he was being set up, but he would certainly know that refusal to do it would mean summary execution. Not much of a choice.