ANSI Z133.1-2006:
"8.1.9 Prusik loops, split-tails, and work-positioning lanyards used in a climbing system shall
meet the minimum strength standards for arborist climbing lines."
My interpretation of this wording is that the 'Prusik loop', which is a doubled piece of cord, needs to be 5400 pounds. The cord for the split-tail, and the rope for the lanyard need to be 5400 pounds.
But that's my interpretation. This section of ANSI is often interpreted as Tom described. Hence the "...conflicting views on this within [your] circle of climbing colleagues..."
I should also add that tensile strength is not the only factor to consider. Some other important factors are abrasion resistance, heat resistance, susceptibility to UV degradation, and compatibilty with the climbing line.