Generally speaking, the little diesels in a skid-steer are not worth repairing unless it is a relatively minor situation. Having to go into the engine will cost big bucks in labor, so it is usually better to just replace them with a new "crate" engine. With the crate engine you get a much better warranty, plus you know everything in it is new. It's also much faster to replace than to rebuild.
It sounds as tho the dealer is trying to make amends, but were I you, I'd insist on a new engine, at as much their expense as you can get.
As for buying used equipment, I always took my own oil samples if I could before buying. If I couldn't, then I did them immediately after getting the machine home to the yard. I never trusted the sellers samples, unless he had a long history of them with none missing towards the sale date. I also checked with the manufacturer's dealer for service data and hourmeter readings, anything they might have on hand. That's not hard these days, was difficult 20 years ago. Getting oil samples really saved my butt a couple of times. For a small contractor or equipment owner, paying 15 to 20 bucks for a sample is good insurance, and better proof.
Good Luck with this deal. Let us know how you come out. Keep the heat on your seller for relief!