This is correct, to an extent.

The undergrond "production" geology team usually sends their samples to the mine lab, which is an unlicensed lab, this is done because of the shear volume of samples that a geology team can produce in a short period of time. Mine labs process samples very quickly and only worry about mucks (samples taken by the trukers/muckers as they empty out the stope), chips (samples taken by the geologist at the face), sludge (samples taken by the mill for quality control) and core (as logged by the underground geologist in order of priority). the turnaround time for priority samples is 12 hours, pretty much as long as it takes to dry, crush and assay the rock.

Underground results of drilling from production stopes has to be done very quickly in order for the vein to be modelled, mined and cost/value estimates to be made, this is why they use a local lab.

Exploration drilling though is a different story, their samples MUST legally be sent to an accredited lab to be processed, this means it must be split in half first (something a production geologist doesn't worry about as they usually send the entire piece of core to the lab).

Accreddited labs can get busy and the average turnaround time for a batch of samples is 10 days to 2 weeks at best, sometimes it can be over a month.

Hope this helps clear things up