That sounds more than fair to me, and sounds like the shop is doing his best to make you happy.
Fwiw, most shops have very explicit wording in their warranty boilerplate covering exactly this situation. In most cases, shops only offer any kind of guarantee on the actual items they replace. In your case, they replaced the overflow reservoir because it had an issue with excess pressure/plastic fatigue/overheating that caused that part to explode/crack. Essentially, you brought them a car that had an issue with the cooling system. They fixed the obvious problem and observed it working correctly. Whatever root problem that is stressing the cooling system simply took out the next weak link, which is common.
I realize that you are putting a lot of weight behind their statement that the cooling system was fine, so maybe it might help to look at it from their perspective. You brought them a broken car, and the basic fix probably cost a couple hundred bucks. That car, anecdotally, has several plastic wear parts that could fail around the same time, however, if you bring them a car with a $200 part broken and they tell you to replace the radiator, the hoses, the head gasket(s), the seat heaters, and the gas cap you will probably accuse them of inflating the bill. If the idea that the plastic parts are wearing out is the correct one, then the shop was absolutely correct in telling you that the cooling system was operating correctly and in spec when they finished working on it. They could have pressure tested the radiator, and had it hold up fine, but I doubt they pressure tested it, because they would have had to bill you for that. It's very likely that they simply put it back together and observed that it worked, because remember a mechanic is costing you somewhere in the range of $100 an hour. Again, they have to walk a line between chasing all the many things that could be wrong with your car and not making your heart stop when you see the bill.
I've built and maintained a car for racing before, and every time I took a system apart I replaced a large portion of the wear parts. This is what it takes to make sure a car never breaks, and it's hours of labor, testing and effort. Also don't forget a big pile of money. I really doubt that you would be happy if you'd taken your car in to replace the $200 ruptured overflow container and they replaced and tested all the possible things that could be wrong in that situation. Your bill for that would have likely been closer to $5000 just to sort out the cooling system. No shop "diamond" certified or not, is going to give your car this extreme amount of care without billing you for it. They usually work hard to get the repair done in as little time as possible to keep your cost down.
You just had bad luck, but pretty much bad luck that should be expected when buying a used luxury car, especially a german one. They break, a lot. I've spent more on repairs for my used audi than I spent buying it, the only reason I keep it around is because it's an amazing snow car for trips to tahoe. That, and the Subaru wagons of the same vintage have a known head gasket issue I wanted to avoid. If I wanted a car I never had to repair I'd stay a million miles away from an overengineered german luxury brand.
I'm actually surprised that the shop is offering to cover this, even though they signed off on your cooling system. If I was you I'd jump on the deal. They didn't replace the part that broke, and the car was in the shop because of a cooling system failure to begin with. I still hold to my original opinion that unless you find evidence that they broke the part, they aren't responsible.
