Did not know that and I am surprised. But it may very well be (out of curiosity, Mark, what's your source?)
A "caffè espresso" means, literally, in Italian, a "quick coffee", and is is commonly said here in Italy referring to coffee at the bar/coffee shop/whatever you want to call it, rather than at home. Which is because bar machines are faster than those at home.
Since it's been like this since I know of (1910s, 1920s, when first steam coffee machines were invented, I suppose), and since "espresso" is such a common Italian word (there's actually a national news magazine called L'Espresso - "The Fast One", or trains: an "espresso" train is a direct one, non-stop, to some destination, and so on), I just assumed that's where the English "espresso" word came from.
Clearly I may be wrong (and, being Italian, I may be unwillingly arrogant and think that all that is coffee comes from here, for which I apologize, should it be the case; but, that's how it is about coffee here; some sort of "national drink" or whatever... We consider it so totally Italian, and we don't even grow it here! ).

And, I did not mean to say that anybody is supposed to know what "espresso" means in Italian. I was just adding info to the conversation.