Be careful of your terms. You are comparing a column in CAESAR II output labeled Axial Stress with the definition of Longitudinal Stress in Paragraph 833.3. That axial stress column is not based on 833.3.
We have a real problem with Codes that define separate rules for Fully-Restrained Lines. To me, a restrained line does not need a comprehensive beam analysis ala CAESAR II - it's all simple slide rule calculations. But you don't really know if it is fully restrained until you analyze it.
Our thermal component of the stress you question is based on "more rigorous analysis" - based on the axial structural load as the thermal strain is resisted by the pipe & soil.