I've always found that to be a silly distinction, like it's a thing that matters to use cases in the same way that axle type matters, but it's not the sole distinguishing marker of whether something is a "truck". There are various non-trucks that are body-on-frame - BMW i3, Ford Crown Vic, Suzuki Jimny, etc. (The highest-spec Jimny tows less than the lowest-spec Honda Ridgeline.)

It is a truck.

Unibody might not be commonly used by truck makers, but using it doesn't mean it's not a truck.

A Tread Unibody bulk truck can haul 50K pounds and no one would call it a ute.