You are in a special situation due to the fact that you are getting your parts from a distributor: Gulf States Toyota (Friedkin Family) who has a chokehold on the Gulf states Toyota parts distribution out of the southern Houston warehouse. They buy their parts directly from Toyota Motor North America (TMNA) which gets their parts from Toyota Motor Corporation (TMC) who buys their parts from the Toyota keiretsu in Japan and elsewhere globally.
The Southeast of the US is also under a "distributor" system-- Southeast Toyota (SET) which is the Moran Family. Same thing as above except the parts come from Jacksonville, FL.
Distributorships are common globally-- parts for operations like Partsouq (which is a parts consolidator and has no connection to Toyota-- they are a software company that happens to sell parts) come from the Al-Futtaim family distributorship in Dubai, who buys from TMC, etc. Saudi Arabia Toyota parts come from the Abdul Jameel Latif family distributor that buys parts from TMC, etc.
In the rest of the US, Toyota has developed a regional depot system that stores parts on their shelves and then sells them to authorized Toyota dealerships in their region (Kansas City, Phoenix, Los Angeles, San Francisco, Portland, Chicago, Dallas, Atlanta, Orlando, Vancouver, Hebron, KY, Cincinnati, Toronto, Boston, NY/NJ, and Glen Burnie, MD). Same with Lexus that pulls from dedicated Lexus depots and Toyota depots, depending on the part number.
There are two more important depots in the US that operate as the big depots for the entire US: Hebron, KY for east of the MS and the Ontario warehouse in Ontario, California: (AKA: the Japan warehouse). It's called the Japan warehouse internally because all depot stock of Japanese parts comes directly into the free trade zone at the Ontario warehouse and is then distributed nationwide to the other warehouses. The Ontario warehouse is the only place for inbound Japanese/global service parts manufactured by Toyota and its parts suppliers which is send to dealers directly on back-order. From there the parts are distributed nationally. The Ontario warehouse is also the supplier of most service parts for the Western Hemisphere. Think vehicles like 4Runner, Prius, Land Cruiser, and other Japanese/foreign manufactured vehicles-- for example, the Turkish manufactured C-HR when it was still sold in the US
The Hebron, KY warehouse is the main warehouse for all US/Mexico/Canada manufactured parts and those part suppliers send their stuff to Hebron for distribution nationwide to the other depots and also directly to Toyota dealers nationwide as well (think parts made for Camry, Tacoma, Tundra, Corolla, etc.-- US manufactured automobiles).
Then there are instances where the part is shipped directly from the supplier to the end customer (critical, vehicle-off-road-- VOR instances). This is generally done via air freight using Toyota-associated logistics companies: for example, 11400-66041 short blocks will come via air freight from Yamato Logistics which gets the short block from Toyoda Industries Corporation which manufactures the short block assembly. These types of situations are rare.
Most often, parts will always come directly from the Ontario warehouse if the part was manufactured in Japan by one of Toyota's many Tier 1 suppliers (Tier 1 suppliers are folks like Aisin, Denso, Toyoda Boshuku, Koito, Toyoda Gosei, Toyoda Industries Corporation, Murakami, Aichi Steel Corporation, etc.)
There are all rules for how Toyota service part support and logistics occurs. These are all encapsulated in Toyota Engineering Standards-- **the** billion page book that governs how Toyota operates its global operation and keeps everything standardized so that a part in Dubai looks and feels and operates exactly the way it does in Thailand or in Germany or in the US.
Outfits like Partsouq, Amayama, Megazip, etc., are all parts consolidators that operate as middle men. They are basically software companies where the product is a widget in a box that gets shipped to an end customer-- but they too are buying directly from a Toyota dealership; there is no secret sauce in what they are doing. They have things like free trade zone, taxation, currency, and logistic relationship advantages that US dealers generally do not have.
EDIT: in terms of service parts pricing that the OP was mentioning: All Toyota dealers globally operate as independent businesses. They can charge whatever the market will bear for parts. Toyota has an MSRP for each country and region dictated by TMC in Japan that is sent on down the line to Toyota Europe, Toyota USA, Toyota Africa, Toyota Australia, etc. Pricing is **always** set by the final entity that is selling the part to the consumer. They have free reign to price parts however they want. Has always been this way. Will always be this way with Toyota.
EDIT 2: "why you get parts faster from the GCC say then the dealership down the street": this is just plain old supply/demand and global logistics. Parts are stocked based on how fast they sell. If parts sell really fast and are popular, they are on the shelf at dealerships vs. depots (which takes anywhere from 1-3 days to get). Land Cruisers are ubiquitous in the GCC, ergo, they have more of these parts in stock and ready to deliver/sell. That is not the case here in the US where the Land Cruiser has always been a low volume seller vs. a Corolla or a Tacoma. Again, none of this is rocket science. It's merely supply and demand and how the global logistics system works today.
” , as the parts guys call it, for my cruiser, they say it has to come from California. 
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