A British family whose hire car broke down on the last day of a French holiday after the engine failed have accused Hertz of bullying after it insisted they return to south-west France to attend a meeting – and warned them that if they fail to turn up they would be liable for a bill of up to £3,750, with no right of appeal.

Jamie and Sharon Ryan, who live in Plymouth, were issued with the bizarre demand more than a month after they returned from a week in the Dordogne.

The couple, who both work and have a two-year-old daughter, Erin, say it is tantamount to bullying.

Fearful of the financial consequences of doing nothing, they say they have spent hours dealing with the matter, and have had to pay €400 (£285) to engage a French mechanical expert to fight their case at the meeting which was scheduled for this Monday in Bordeaux – despite knowing they did nothing wrong.

For many people, car hire is the most stressful aspect of their holiday – and coming back to find a bombshell bill for thousands of pounds for something you didn’t do is the ultimate nightmare.

Car hire experts told Guardian Money that this is the first time they have come across a demand of this type, and say the threat that someone would lose their right of appeal is wrong.

Happily, after Money intervened this week, Hertz has had a change of heart. But it shouldn’t have taken our intervention for the company to see sense.

The Ryan case comes just weeks after it emerged that five of the biggest car hire firms, including Hertz, had agreed to make changes to their terms and conditions following concern about hidden costs and “potentially unfair” practices. This follows a Europe-wide review by the UK’s Competition and Markets Authority, which has been monitoring the sector closely in response to a steady increase in consumer complaints about car rentals. The case also highlights the need to buy a decent third-party insurance policy to cover just this sort of eventuality.

The Ryans were holidaying with another couple, and picked up a Ford C-Max at the Hertz office at Bergerac airport. They diligently checked it and noted damage to the front bumper which, they say, looked as though it had been caused by a minor accident. The paperwork was signed by a Hertz rep, and off they drove. They say they then “pootled” about, rarely driving further than 20km in a day.

On the last day of the holiday as they were driving slowly through a village, the engine suddenly cut out and they coasted to a halt. The car would not restart and the console was illuminated with “Go to Ford dealer”.

Hertz’s breakdown assistance arm sent a tow truck 90 minutes later. The mechanic couldn’t start the car, but wouldn’t give them a lift back to their gite just a few miles away. He left with the car on the back of his truck.

“I spent the final hours of my holiday arranging for Hertz to provide a taxi to Bergerac airport,” says Jamie, a freelance cameraman. “When we got there I walked into the Hertz office to introduce myself. The female employee apologised for the breakdown and provided me with a Citroën Picasso to use for the last few hours.”

He thought little more about it until, 11 days later, he was contacted by Hertz and asked to fill in an accident report form. He said that wasn’t necessary as there had been no accident, merely a breakdown. “I completed the report in good will, thinking it would assist in the repair, but was then staggered when the company wrote back demanding I attend a meeting on 24 August.

“It states that it will determine liability and warns that if I, or a representative, is not there, I would lose all rights to contest the appraisal or my liability. If it wasn’t so serious, you would have to laugh at its ridiculousness,” says Jamie. Hertz told the couple that a new engine would cost up to €5,300 (£3,750).

Jamie adds that he can only conclude that the previous hirer damaged the car, and that it hadn’t been checked properly when returned. Photos of the damage sent by Hertz suggested it happened previously, he says, but he can’t prove it.

“I’m no mechanic, but we didn’t cause it. On the day we broke down we had only been to the local baker for croissants. No oil lights came on and there was no warning. One minute we were driving along, the next we weren’t.”

He says his requests for Hertz to provide service records or maintenance information have not been met, nor has it commented on what pre-hire safety checks were carried out.

“The whole episode has been ridiculously stressful, and to me looks as if the company is relying on the fact that we can’t just drop everything and attend a meeting in Bordeaux.

“I don’t even understand why I’m being asked for up to €5,300. The excess on the policy is €1,500 (£1,060) and according to the Hertz website the rental covers damage.”

Hertz told us this week that it was the highly unusual nature of the breakdown that had led it to call the meeting – although it concedes it should never have told the couple their right of appeal would be lost if they failed to attend. As a result it will no longer be chasing the Ryans for the money.

The company says its mechanics thought it unlikely the car would have been able to be driven without incident for six days. However, the lack of oil on the road suggested the cause of the damage could not be easily determined.

“Hertz decided to carry out a appraisal with an independent third party expert, at our expense, to determine the likely timing of the damage. The customers were rightly invited to attend, in person or through their representative, to witness the appraisal (even though this is not a requirement),” said a spokesman. “It is clear that our policy was not adequately explained to the customer who was also told, incorrectly, that they would lose their ability to contest the independent appraisal if they did not attend. Given the unnecessary anxiety caused by this incorrect statement of our policy we have decided not to charge for the damage, even if it is subsequently determined it was most likely caused during the rental.”

Hertz has also agreed to refund the money that the couple spent on hiring a French technical expert.

Why insurance is the best policy

The Ryan case could almost act as an advert for the car hire excess insurance products Guardian Money has long urged readers to use.

Car hire firms are fast becoming one of our most complained-about areas. Yet readers can remove 99% of the stress by buying such a policy. Had the Ryans had one from Money’s top choice of provider – insurance4carhire.com – they could have simply handed the matter over to them.

Users pay £39.99 for a European annual policy that covers every rental in a year that lasts up to 60 days. Buyers then need to decline the excess or “super collision damage waiver” at the car hire desk – no mean feat in itself. If you crash, or damage the car, you pay the firm’s excess and reclaim that from insurance4carhire.com

And unlike a typical car hire firm’s own excess policy, it covers damage to wheels and tyres, mis-fuelling, towing fees, and the underside of the vehicle. It told us this week it would have covered the Ryans – and paid out, had it come to that – and negotiated on their behalf with Hertz. This is one product Money writers buy themselves.