They can now a days find you had a tune even if you remove it. And yes they can void the entire vehicle warranty not just the engine. And if you fight it you better have better paid lawyers than Ford has in order to win and that's gonna cost ya.
With respect to the engine, computer systems, emission controls and exhaust, I would say yes. For the car in general, maybe. I feel it's going to depend on the area being considered for warranty, the dealer and your unique experience. Several threads/posts on this topic. Recommend perusing those and studying in detail.
*Edit: BTW, I see LA has emissions and vehicle inspections in some areas. I'd read up on that to.
In order to void the warranty they have to prove your tune caused the fail. If the tune runs too lean (or even just more lean than stock) they can say your tune causes engine damage. They can’t void warranty on something unrelated because of it. You could argue the warranty on the computer system that holds the tune could be voided easier than anything else.
Let’s be real. You didn’t buy a mustang for the warranty. Just do the tune and enjoy your car.
It's really simple. Ford warranties the car that Ford built. When you modify it (i.e. change the tune) it is no longer the car that Ford built. If Ford determines that your modification caused a problem then they will deny coverage for that repair.
As far as Ford proving it --- they send their determination that your modification is the cause. End of their proofs at that point and Ford doesn't need to do anything else. It is up to you to start the lawsuit, hire your experts, and present your evidence that Ford's determination is wrong. At that point, assuming you put forth sufficient evidence to avoid a motion to dismiss, Ford has to bring forward more evidence.
If you changed the stereo to an aftermarket one, would you expect Ford to honor the warranty on the audio system?