My worst experience of "Not covered under the Warranty" was when I'd taken out an extended warranty with a major 3rd party provider who sold me on their USP (Unique Selling Proposition) that unlike other 3rd party providers they would cover "Consequential" secondary damage/failure. The example given me was that in the event that a Fan Belt broke and bits of the belt fell into the Cam Belt which would brake the Cam Belt which in turn would trash the valves and head they would cover all the damage not just cover the Fan Belt. Pretty daft you agree and you'd expect all the "Consequential" damage to be covered, wouldn't you.
Six months later my Renault Diesel was running badly and I had the AA out 3 times in one week. The fault codes said low fuel pressure was caused by a failing fuel-pump and consequential damage to the Diesel injectors. Covered right? Wrong The failing fuel pump had caused fine particles of metal to be carried around the fuel system and these would be sticking the in the insides of all the fuel lines injector manifold filters return pie and fuel tank and the whole lot would need replacing at a cost of £3,700 +VAT. The company offered to replace the Fuel pump £180 including labour but not any of the rest of the system, not even the main fuel filter. WHY? Because "Fuel Contamination" was a specific exclusion. They argued that everything apart from the pump was due to contaminated fuel and that exclusion included any type of contamination.
This kind of failure is apparently a common failure of high-pressure common-rail diesel fuel systems and can happen any time after about 50,000 miles. Peugeot even supplies the entire fuel system in one box with all the pipes, filters and valves all laid out in the correct position to be fitted to the car, so common is this issue.
Fortunately, my local Independent Renault workshop who had regularly serviced all my Renaults, fitted the pump and filter and flushed the fuel system best he could but warned he couldn't guarantee how long it would last as it would be impossible to completely remove all the contamination. So I paid a couple of hours extra labour for the decontamination and drove the car directly to a car sale dealer to PX it for a petrol car. I got £2,500 against a good used Peugeot 3008.