Exactly and precisely 0.0% of printer manufacturers make their own ink.
Almost all printer ink in the world comes from a very small region, a single business park really, of Malaysia. Some is also made in Europe and Japan.
It is made by companies like Toyo Chem, DIC, Sakata, and Swan and transported directly to the facilities that fill the cartridges.
Printer companies have almost no input into the process, they buy based on spec from a list of offerings.
3rd party cartridge manufacturers buy the same ink, with the same specs, from the same manufacturers as printer manufacturers.
If a printer manufacturer claims to have an exclusive formula they are either lying, or the ink maker lied about giving them exclusivity because you can buy any ink from anyone at anytime. If the manufacturer wants to keep up appearances they'll change a single digit on the product ID and claim it is a different product, they don't care where the drums are going so long as the wire transfer goes through.
Even the ink manufacturers OFTEN don't "create" ink. They just blend pigments from pigment manufacturers together with solvents from solvent manufacturers in formulae that are pre-determined between the pigment and solvent makers.
If a customers says "I need an ink that does x" they go to the pigment and solvent suppliers and ask "what do I need to buy so the ink does x" and the suppliers tell them and the ink manufacturer follows the formula to the letter.