If I had large sums of money, I’d bet a LOT of it on that chestnut having some serious hock issues (or possibly even farther down to the fetlocks, or both) and the not sitting not having anything to do with a flat croup.
I’ve always been told the same thing, and have always found the flat-crouped horses with good hocks and good training have no more difficulty truly sitting than horses with ideal croup conformation.