Why do people think this?

Can you find any annual report from a car manufacturer that shows parts sales contributing significantly to profit?

Yes, dealerships make money from servicing and parts: "the service and parts department, which accounts for the other 49.6% of the dealership's gross profits".

But a car manufacturer doesn't capture that, so a manufacturer has no financial incentive to increase profits for dealerships.

Well, I hope to god AC Delco makes at least some profit from selling parts.

  ACDelco is an American automotive parts brand owned by General Motors

It isn't clear that AC Delco would have any incentive to supply bad parts so that AC Delco could sell replacements and profit.

FYI Toyota owns an equivalent parts supplier called Denso.