Cochrane didn't get that close a look or maybe he wanted one more like it but they didn't have the budget, the brass is usually like "we don't want the best.... we want the best we can afford".
As far as canon goes. They always refered to the Federation's first contact with the Klingons, not Earth's, you can take it to mean the whole Broken Bow and subsequent events didn't help, when the Federation ship, representing multiple adversaries, made diplomatic overtures and all they can remember is the criminal Archer... Klingons live longer and hold grudges forever you know....
"Retreat?! Hell, we just got here!", annonymous American Marine, WWI
"Gravity is a harsh mistress....", The Tick