I'd take it as meaning 'sub-contract', but strictly it means to sub-lease, as in property. I've never encountered it used in this fashion. It might be regional variation, or it could be butchered legalese.
It means the smog check station cannot sub-contract the inspections to another party. They must do the inspections themselves. This use of 'sublet' as a synonym for 'sub-contract' is reasonably common in my experience.
in the meaning of sub-contract, could it be implied that this phrase works both ways. Meaning that a station may not accept sublet inspections from another station nor may a station send sublet inspections to another station