Hi
If it's a greeny-grey colour it's ordinary primer. Fiat seemed to manage to get primer to stick but weren't so successful with the finish coat, especially parts subjected to heat, sunlight, sharp edges etc ! If you rub down enough to form a "key" you should be able to apply a new top coat.
A professional body shop would probably take it back to bare metal so that they know what they are dealing with and can be responsible for a lasting job.
Etch primer is for bare metal, only a thin "dry" coat is used.