Ditto; unless that car was a company car, and the driver was an employee. Damages are inevitable.
If the CFI is eligible to get fired, then he is an employee, and should by default be covered by the company. After the accident is taken care of (at no cost to the employee) the company then should weigh the risk of keeping the employee vs the total worth of said employee (e.g. he has a ton of students and a clean record until now.) I wouldn't want to work for a company that didn't exercise sound judgement in this regard. In this case, I wouldn't pay, but unfortunately that doesn't mean they have to keep you around either. Either way, the CFI should have had a contingency plan for this type of event, it's an inherent risk of being a CFI. I wouldn't have gotten involved with a company that wasn't willing to cover me in the for such a small event in the first place. If it were me, I would resolve the issue, and find a place to work that supports their employees in time of need.
Conversely, if the CFI was quite simply renting the plane from the company, I would compare that to getting a fender bender in a rental car. That's why we get insurance when we rent cars. By default the student couldn't rent something he's not qualified to use on his own, so the CFI is responsible, not the student. Again, damages are inevitable and it's ill-advisable to not plan accordingly, insurance is a must. In this case I would consider the money owed to the company a penalty for not having his bases covered (with insurance) when they were fully loaded. Talking to the owner and trying to get the amount owed lowered would be a good idea here.
There is no possible way it was the line guys fault. The plane may have been moved, but the CFI let his guard down, and hit a stationary object. If the CFI knows the line guy is a risk at times, then the CFI should be exercising extreme caution when around the ramp under that single premise alone. I would compare it to driving a car in a parking lot, you just inherently have to watch out for the people who didn't quite park in their lanes properly, and can't expect all the cars to be in the correct spot ALL the time (because it seems to me, a lot of people are really bad at parking). Again, another reason to get insurance or review the company policy beforehand.
We all choose our battles. I have learned it's best to exercise extreme caution when picking battles, unless your job is on the line; even then, I feel it's important to strive to be the bigger man; it says a lot about one's character. Resolve is priceless, and I don't recommend for your friend to quit/leave without taking care of the dispute, regardless of who is right or wrong.
Pure speculation on my part but I would imagine the accident went like "Go ahead and taxi past that aircraft, I know it looks close but your good, I've done it 100's of times before." Bummer.