I find it a pretty glaring ommission that
LAWA's news release and FAQs page (the latter appears to have been recently revised), and the new LA Times article posted above, make no specific mention of traditional car services. This is LAX afterall....
TCP vehicles/car services (licensed car services should be TCP, but I know there are also neigborhood airport drivers who do dropoff/pickup who may not be TCP) are covered in the last group on page 2 of the LAWA pdf in the skift link posted in the first post. They pick up at the islands at the lower level, same place as your friends and family.
(ETA: it was posted in the equivalent of being "...on display in the bottom of a locked filing cabinet stuck in a disused lavatory with a sign on the door saying ‘Beware of the Leopard.'", but it was there)