The PC should not have used an assessment to find cover behind the car and treat it as an aspect.
The PC should have made an assessment or declaration to find a car and treat it as an object.
In the first case, the car is treated as something the PC can use to duck behind as he is being shot and better avoid the bullets.
In the second case, the car is treated as an object or zone border the PC could move behind before he is shot so that if someone sprays the area with bullets the car gets hit but not him.
In any case, do note that while rules-wise an attacker does not move any zones while shooting, story-wise combatants are maneuvering within the same zone while they fight. If you maneuver casually behind an object during combat, nothing stops an attacker from following if he is attacking you. Tagging or invoking an aspect for cover means that you are putting extra effort to stay ahead of your attacker and thus benefit in your defense.
On the other hand, if someone is not attacking you but is shooting blindly or if someone is attacking you but the nature of the cover or zone border prevents them from following, two things can happen; first, you treat the thing you're hiding behind as an object, with its own stress track and defenses. That happens when you are taking cover in such a way that the object blocks the attacker no matter what he does - i.e entering a vehicle or building or jumping behind a wall while the attacker cannot. Secondly, you treat the cover as a block against the attacker's skill. That happens if the obstacle does not cover you entirely and a shot is possible but much harder.
Example:
In a battlefield, the engineers build a pillbox from within which soldiers can shoot out at the enemy while the enemy cannot shoot back. The engineer rolls craftmanship to see how well he builds the thing. During the battle, someone inside the pillbox that is shooting back is very hard to hit - the pillbox is a block equal to that engineer's roll to oncoming shots, though someone could still shoot through a hole with a high enough roll. On the other hand, if some soldier is cowering inside the pillbox and is not even visible from outside, enemies have to attack the pillbox itself before they attack him; use the table for wall strength in the books to see how much damage the walls can take before collapsing.