I'm not sure the OED is particularly helpful here, as it is very slow-moving, and often imprecise, being more concerned (from what I can tell) with describing casual usage than precision usage (and yes, I do have it; micro-print edition; I'd love to have the full-size version, but I don't have that kind of money laying around. Heh.)  Anyway, I do get your point that there is overlap in genera parlance.  From the OED perspective, there "isn't" any difference at all between these words other than "jargon" never refers to slang.  I think a lot of people would have problems with these definitions.
Anyway, to get back to your real point, if these terms are used more interchangeably in the UK than they are in the US, there is no harm at all in making them more specific/accurate to Yankee (virtual) ears, since there won't be any effect at all on British ones, if you see what I mean.  I think this is especially true in the case of that article because most of the terms are jargon rather than slang (some are of course slangish — "action", "velcro", etc. — but they're in the minority").  And it's not that the OED-based usage of argot/patois/lingo would be wrong from an OED-based perspective, simply vague (the meaning of all three words in the the OED is basically "slang or jargon".  -)  Anyway, glad we're not really arguing. Heh.
—  [talk] [contrib] ツ