This is clearly false. None of Nvidia, AMD, or Qualcomm manufacture their own chips. These companies are valuable despite not having in-house manufactures, perhaps because of it.
Correctness of this statement also depends on the type of chips.
Not everything needs the latest and greatest process node (which is predominately a fabless industry) except for advanced microprocessors, SoCs, or storage. On the other hand, 65 nm is perfectly fine for 90% of chips in existence, even 0.18 microns is still often used. You don't need EUV for a good LED driver, a serial port, or a battery charger controller. If we talk in this context, indeed, companies like Texas Instruments, NXP, ONSemi, Analog Devices, Microchip, etc, usually make chips in-house.
They dont have to outsource their Core Asset. If Intel ships 250M CPU annually there are also 250M Chipset going alongside with it. Those can go to TSMC or Samsung. ( Or in a turn of an event, Global Foundry )