Your thoughts and advice would be appreciated

I'm sorry my post is so long, but I have a situation with my 2010 XK 5.0 Portfolio and would appreciate your thoughts on the situation and any advice you may have.

I bought my XK in Jan this year, a 91k mileage car but with full service history with Stratstone to 80k and indipendant thereafter. I had looked at several and this was the quietest engine and the best condition car with the best history, which is why I bought it.

Anyway, after covering just 580 miles over the next 2 months, one morning as I pulled away from my house, I got the red triangle warning on my dash and the "Restricted Performance" warning, however the car drove unchanged. I stopped the car, turned off the engine and re-started, but the engine managment light stayed on and I contined on my short journey with no issues.

The next time I drove the car, 2 days later there were no warnings and the engine management light had gone off and I drove the car for the next week without any issue, then after about 8 days the exact same thing happened again with the Restricted Performance warning, so I called my local jaguar specialist ( https://www.thejagspecialist.com) and booked it in to be checked.

I should add that I bought my car from a dealer approximately 110 miles away (https://www.reissjames.co.uk/) and as I thought it would just be a sensor or a glitch I thought I would use my local jag specialist.

On my visit to the jaguar specialist I got a massive shock when they told me that it would need a full engine strip as the fault was either the cam chain, the VVT's or another related item that I can't quite remember, but either way, the cost would be approximately £3,500!

Now the supplying dealer did give me a 3 months RAC warranty, however this only has a claim limit of £2,000 so it was at this point I contacted the supplying dealer, Reisse James, and asked them what my options were, as clearly I should not be expected to pay the difference in the bill after such a short time and so little mileage.

Anyway, the dealer decided that they wanted the car back with them so they could assess the car themselves, now I will add that although the fault code was stored in the ECU and wasn't cleared by the jag specialst, the warning or engine management light has never come back on whilst using the car for the next 8-10 days at which point the supplying dealer has now collected the car and has had the car since Friday 8th April.

The issue I now have, is that the dealer is saying the car drives fine (which it does) and as the warning hasn't come on for them (although the fault code was stored in the ECU), they do not want to do anything and want to return the car if the fault doesn't show for them. 

So my problem is, even if the fault did show for the dealer, all it would give them is the same fault code they have already seen on receipt of the car, so why wait for it to re-occure? surely they job that the jag specialist say needs doing, still needs doing?

Or is it just a spurious electrical glitch and not a real fault and the jag specialist were just trying to get a £3,500 job from me?

When the fault occured and the car was uneffected, my thoughts were that it was just a glitch or a sensor issue, but to then be told by the jag specialist, no it needs a full engine strip to diagnose which of a possible 3 items it was and either way, it would be around £3,500 was shocking.

Your thoughts and any advice would be greatly appreciated 

P.S. I have included a pic of my ODB reader screen too although this is just a basic reader