Regarding crude sourcing, when I used to refine the stuff for Esso (Exxon) in the UK, we used to get it from all over but mainly from the North Sea & Middle East. There's a lot of very complex science that governs what crudes you buy & from where (linear programming driven process economics modelling). However, the golden rule is if you can buy the right crudes (in terms of density & sulphur) locally at the right price, then you buy local.
Lube base oils tend to differ from crude oils. You tend not to buy run-of-the-mill base oils in, for example, Saudi to use in the US because the transport costs become very significant. As a rule, local base oil production tends to feed local supply. Shell produce Motiva stocks in the US (at Port Arthur as I recall). However, because the US is so vast, it doesn't necessarily make sense to ship the stuff all over the country, so a bulk Shell fully formulated oil grade might be made from one of several base oil that are available locally. A Shell oil in California might easily be made with base oil made at Chevron's Richmond plant, just because its cheaper & more efficient to do it that way.
However there are exceptions. Shell GTL base oil ALL comes from Qatar and is made exclusively from Qatari natural gas. Likewise a huge amount of Group III traditionally comes out places like South Korea.
