I meant to do some more research on this, and kind of let it get by.
In general, if the load is a specified load from a building code and just referred to as a "design load" or something of the sort, then I would agree it would be be designed just like other members of the building or whatever it's on, as noted in the other posts above.
In looking at the OSHA requirements, they say the handrail is to "withstand" a 200 lb load, and of course, don't specify any design code or method to be used for it, and that leaves it fairly unclear. OSHA also specifies a 2"x2"x3/8" angle or member of equivalent bending strength, or a 1.5" "nominal" pipe, which they interpret elsewhere to mean 1.5" OD. Anyway, using 2"x2"x3/8 posts, I think gives 24,000 psi if the load is on a single post. Using 1-1/4" pipe gives 36,000 psi or so. In both cases, that would seem to exceed allowable AISC-ASD stresses, but does not calculate as a failure, either.
I'm not sure where the "should not fail" wording comes from, if anywhere.
The NAAMM publication mentioned above addresses the question on pages 15 and 16, with the authors agreeeing with the other posts above.