The links to America, and creation of the 'Uncle Sam' moniker ( allegedly after a New York meat dealer) might naturally have brought up the similarity in nicknames as networks grew. It is certainly true that the close links between Liverpool and America would have encouraged the overlap in terms, and it was certainly claimed wholeheartedly and proudly by Liverpolitans.
Outside Liverpool, it was used as a term of insult for exactly the same reason. Just as a 'dickey' is a fake shirt, inhabitants were seen as wannabe Americans by some of the London merchants, hence 'Dicky Sam' as a term both of affection and derision.