The release is electrical, irrespective of whether unlocking with the handle or the remote; if using the handle, then a microswitch inside the handle completes a circuit to send the control signal.
The extremely common hatch wiring failure is responsible for the vast majority of boot opening issues. But if it unlatches normally using the button on the remote, then the power to release the lock must be getting passed through the loom. So in this case, it could either be a partial loom failure preventing the control signal from the microswitch from passing, or a failure of the microswitch itself.
Microswitch failure is also quite common, as its position inside the handle means it is easily compromised by both dirt and corrosion.
If you want to investigate further yourself, first disconnect the battery from the car using the quick release on the battery terminal. This is important; messing with a faulty loom could cause a spurious electrical feed to be passed through one or more of the car's electronic modules and this could result in considerable collateral damage.
Then peel back the grommet where the rear hatch wiring enters, and inspect the cables carefully for damage or signs of a previous repair. If all is sound in that area, then you need to check the handle is working correctly from an electrical point of view.
Replacement handles aren't cheap, and the individual parts aren't available from Fiat or the motor trade, but competent DIY folks can dismantle the handle and replace just the microswitch; something suitable can be sourced from the likes of Farnell or RS components. You can also try using a contact cleaning spray on the microswitch (and doing this periodically could prevent premature failure), but don't use WD40 as it may damage the plastic components, as well as leaving a sticky residue which will attract more contamination.