1) Are you in a part of TX subject to the UPC, rather than the IPC?
2) 5' maximum for a 2" trap arm is indeed the UPC requirement, while IPC is 8'.
3) Immaterial. Passed inspection means "no code violations found," not "no code violations present." If you've found a violation, they need to fix it. And so far no one has explained why the trap below the floor isn't a violation. [Because it is a violation.]
The discussion about trap arm length refers to the horizontal length downstream of the trap. Your concerns are about the trap location in relation to the sink outlet, the upstream side of the trap. So they haven't addressed your concerns.
BTW, the UPC citation for maximum vertical distance between the sink outlet and the trap is here (a link to the California version of the UPC, because up.codes only lists the IPC for Texas):
https://up.codes/viewer/california/ca-plumbing-code-2019/chapter/10/traps-and-interceptors#1001.2
"The vertical distance between a fixture outlet and the trap weir shall be as short as practicable, but in no case shall the tail piece from a fixture exceed 24 inches (610 mm) in length"
To put it succinctly, they need to respond to "The current kitchen trap location exceeds the maximum 24" vertical distance from the sink outlet to the trap per UPC 1001.2. Please fix this violation or provide a code citation showing an exception to UPC 1001.2."
Cheers, Wayne