Why use "Greek" text at all? Why not just
Google about for some relevant, similar text and copy/paste it into your layout? It has to do with
intended misdirection.
People are notoriously content-focused. Real or near-real content draws people in. Even though you'd like to engage them in dialogue about the philosophical implications of your font choice, carefully considered leading, intricately art directed images, sculpted gutters, and exquisite color palette, it won't matter. They will spend your expensive meeting endlessly dissecting the content: where it's right and where it's wrong. Where it's missing the point. Where it pertains to their company and where it doesn't. And you can't blame them entirely. It's what they know. It's where they're the most comfortable.
In order to get them away from the content, you need to replace it with something else. It can't be too overt (e.g. blurring the text or replacing it with gray blocks) or it will still draw unwanted attention in a review and what's worse, affect the feel of the design.
Replacing it with a foreign language should do the trick, but you need to choose the right one. Pictographic languages are too graphic, too unusual. The language should use the Latin alphabet. French and Vietnamese have the right letter shapes but far too many diacritical marks. Dutch and Finnish don't have as many diacritical distractions, but their unfamiliar vowel usage still distracts the eye. Italian might work except that the word lengths are much longer than English. Latin, being one of the parent languages of modern English, has no distracting ornamentation and creates boumae quite similar to English and so is a good choice.
Once you've found a language, you only need to find a large chunk of the stuff that will fill out your design. Lorem ipsum is handy because it has been, as interrobang notes, an available resource for the past 400 years. Resources such as www.lipsum.com now exist online to spit out long column inches of the original text to fill out nearly any space you need it to.
With the fake text in place, your audience will be able to focus on the elements of your layout on which you've worked so hard.
This overarching principle of misdirection works for any content in a hypothetical setting, e.g. tables and graphs in annual reports, usage scenarios in interaction design, and even lyrics in song composition. Make the content plausible, inscrutable, and forgettable, and your audience should be able to focus on the parts you want.