So specifically if 'fabrication' is chosen where a simpler word would do, or chosen to contrast with a simpler word, then it acquires increasing implication of falsified/counterfeit work.
If you (or more likely an large team/firm) can 'fabricate' a 'car', good job, you're skilled.
If on the other hand you 'fabricate' a 'paper' or 'result' or 'fact' or 'photo' or 'logo', you're involved in something shady.
This factory fabricates iPhones.
vs.
The fabricated iPhones came from this factory.
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.
It's a little bit of an uncommon/sloppy usage, but still clear... more likely to appear in impromptu speech than writing.
"The fabricated news came from this propaganda ministry" works perfectly, however
"...make an elementary analysis." [strongly implies 'do the necessary work']
"...make up an elementary analysis." [might mean 'do the work' but has some implicature of 'improvise from your imagination']
On the other hand, 'whip up' is merely an idiom for 'bring together quickly', and so "...whip up an elementary analysis" would again have no implication of faked data (as opposed to real data collected quickly).