NEC 210.8(B)(2) Code Interpretation

[tortuga]

Is the "spider box" part of the premises wiring system?

Yes the definition of premises wiring system includes 'temporary' wiring', even outdoors.
See the definitions of premises , and premises wiring system.

The spider box, not being itself a permanent element of the distribution system, is the utilization equipment.

I must respectfully disagree based on the way I read the definition a typical spider box would not meet the NEC definition of 'utilization equipment'.