Well, according to my ITIL book, a Service is "A means of delivering value to Customers by facilitating Outcomes Customers want to achieve without ownership of the specific Costs and Risks."
So according to that definition SaaS is: a company would buy that wants to get the outcomes a particular piece of Software can produce, but doesn't want to assume the direct costs and risks normally associated with purchasing, installing, running, and maintaining that software. So based solely upon the denotative definitions of the words, it is not illogical.
And if you think about, back in the early days of computing, most of it was done on a sort of SaaS basis. You'd buy the service from somebody with the mainframe, and run it on their mainframe according to the agreement.
I suppose in some instances, there still might be some business cases to be made on that model. What I see as the major problem is that these days SaaS seems to be intent on pitching things like replacing your word processing suite with Saas. And to me, that makes no business sense at all.
But yes, they do seem rather intent on mutilating the English language, and both sides of the pond seem to agree about that point.