zdad – First, if you’re going to abbreviate my SN, then it’s JMH (not JMP). 😉
Second, I did as suggested and did a quick google. Hopped around a few etymology sites and it does seem like the origin of the word soccer is as you suggested, but is not from the 1850’s – according to most sites I found it dates to 1896 and the story attributing it to an Englishman is likely apocryphal. The word football as describing the sport from which modern Association Football derives dates back to the Middle-Ages (earliest reference is 1280). It seems (according to a few sites I found) that the word soccer was actually a reference to the associations themselves and not the game, and was attributed to the game by your lot across the pond. So, all in all, it seems fairly clear that football was always the name of the game. It may be that some people called the game itself soccer much later (a good 40 years after Association Football became codified and popularised) or that the nickname given to the associations was applied to the game. Either way, we invented the game and we decided to call it football. So there :-p.