That is normally a job for the pilot. Even the SkyWest pilots that fly the Embraer 320 from Pocatello to Salt Lake City for Delta Shuttle perform basic check like that. I don't know if the big Boeing/Airbus jet aircraft get a similar fuel check by the pilot. I do see the pilot-in-command walking around the whole aircraft for a pre-flight.
A private pilot does that as a point of personal responsibility. A student pilot would perform those checks under the instruction and supervision of a proper instructor.
Thanks again.