Yes, but adding an extra dimension to a given space (more correctly stated as asserting that a space of dimension d is embedded in a space of dimension d + 1) vastly expands the "number" of points that are available, so adding a dimension doesn't just give you access to an additional d-space but to a whole continuum of other d-spaces. I think this is what people are referring to when they use the word "dimension" in this kind of context.

Moreover, I don't care about what people think they're saying with their crap terminology. I demand actual accuracy, or at minimum precisely delimited uncertainty, from people taking millions of dollars in government funding to write about aliens. This is not too much to ask. (You do remember the context, right? Evaluating the credibility of a purportedly factual report written under a government contract, not a bar debate about cosmology)