Meh. When I say "cloud", people understand that whatever it is, it exists "out there", and not in some server in the basement of my office or as an app they need to install on their computer/device.
Nobody cares about the more fine-grained terminology, and in fact they shouldn't be expected to. This is nothing more than a purist rant.
Of course, if they demand a "private cloud" (WE CAN'T JUST LET AMAZON STORE OUR DATA THINK OF THE CHILDREN), then it's just on several servers in the basement :-)
Because it doesn't matter what is it based on. Important is _where_ it is. I mean, yes, instead of "in the cloud" you could say "out there", but that's more confusing, because can mean too much things. Cloud is a nice word that does it's job well.
Nobody cares about the more fine-grained terminology, and in fact they shouldn't be expected to. This is nothing more than a purist rant.