Neary: Rotten to the (Open) Core?

I doubt that. I suspect the often blamed double meaning of the word "Free" would work against that.
Whereas a loosely knit community of many individuals has no problem explaining the two different meanings over and over again to different people (using the speech not beer catch-phrase, which is quite humourous the first time a person hears it, and catches their interest), for a commercial company it would require a real expense to make a differentiation between gratis and libre. What's more is that they need to establish that first and from there on distort the term "Free Software" for their own purposes, but by that time they have already educated their customer, and it would be a lot harder to mislead them.

With the term "Free Software" you cannot skip on explaining why "Free" doesn't mean no cost, especially in a context where you would try to maximise profits by distorting its meaning. But once you explain what it doesn't mean, you can't just leave it dangling there; you'd have to give an explanation what it *does* mean. It's probably possible to distort the meaning there, but all in all the process to distort would be more laborious and error prone and as such less profitable.
The term "open source" is far more monetizeable, which I think is one of the reasons it was adopted quickly, but for the same reason it is unfortunately also more vulnerable to corruption.