engine chain

engine valve timing chains normally last the life of the engine. Yours look like new with very little wear. You say "at service". Was this car towed in dead on the road, or was it driven in?. If it is drivable, nothing they said is true. Nothing. Get it out of there and don't go back. Scammers they are.

Agree with Hornet if vehicle was driven in for service chain can not be broken vehicle would not start and like Hornet said chain should last the life of engine as long as oil has been changed at the recommended mileage.

If the engine is running then the timing chain is intact. Take it to another shop for a second opinion. Timing chains with wear on them or are 'stretched' will throw timing related codes, in addition you may see codes for the knock sensor or potential engine shut down when operating. You might also have an intact timing chain but a broken or worn tensioner that can cause problems as well. Let a certified and trusted mechanic look it over.

BMW's with the 4.4 V8 are prone to timing chain guide failure. it is rather common to see guides fail around 120k or higher mileage. You can drive a car with shot guides for a short time, however not repaired eventually you'll destroy the motor. I have changed a couple sets of (timing chain) guides on BMW's with the 4.4, it is a huge job that requires specialized tools. DIY costs are around 6 to seven hundred. Dealership costs start at 3,500$ and up. From your description IMO your problem is timing chain guides.