When physical objects are fabricated, it means they're created. "Fabricated" never means "of fraudulent provenance", like your iPhone example.

When statements-which-purport-to-be-facts are fabricated, it means they're falsified. So "his claim (that these phones are iPhones) was fabricated" does mean that the phones are not truly iPhones.

As I consider it, this makes some sense; you cannot create a fact, but you can create a physical object, and you can create a lie. Things like an analysis are on the border. And indeed, my intuition as a native speaker accepts "fabricate an analysis" in either sense.

Never say never; I think most American speakers would find that the 'fabricated iPhones' noun phrase implies that the iPhones are counterfeits. Otherwise the adjective would be awkwardly unnecessary – all iPhones are already manufactured. So, it must be there to emphasize (or at least hint at) the other meaning of 'fabricated'.

It's a little bit of an uncommon/sloppy usage, but still clear... more likely to appear in impromptu speech than writing.

"The fabricated iPhones" simply means the iPhones which were made.

"The fabricated news came from this propaganda ministry" works perfectly, however

'The fabricated iPhones came from this factory', where 'fabricated' means 'produced', is a tautology and hence an ungainly way to present such a sentence ('unfabricated iPhones' wouldn't 'come from' anywhere). As presented, I feel it's more likely for 'fabricated' to mean 'fake', given the context.

I don't think "fabricated iPhones" means fake iPhones at all. It might be awkward, but that doesn't mean that it means 'fake'.