Jean Louis,
You keep assuming we don't understand the terminology. We know full well the distinction between Free/Libre/Open-Source/Gratis/etc. Most of us have been involved in the Free Software community for over 1-2 decades.
The thing is, if we were trying to convince only extremely hardcore people, there would be no need for the PureOS web page at all, it would be preaching to the choir. I expect they wouldn't even be running PureOS anyway because they're so well-versed and accustomed to their own systems. Instead, the point of this OS's existence is to attract new users to the Free Software movement with an OS that appeals to them on a technical and usability standpoint while respecting their freedom. You don't do that by being un-understandable by anyone but the geekiest of geeks. If you are so restrictive, you will remain a small stagnant pond. Nobody benefits from that.
Nowhere in there is "open source" mentioned alone and carelessly like you depict it to be. It's always "Free software" or "Free/Libre and Open-Source". There is no issue with that. There is not even a mention of the verboten word "alternatives" in there, unlike what you claim. And when you pointed to a Google cached page, it's an ancient version of the old website, multiple weeks old (with multi-months old contents, actually), hardly relevant to this discussion; and websites are not meant to be frozen in time for all eternity.
And again, this whole thread is about the software distribution. Is it Free? Yes. Does it promote user freedom? Yes. Then it is ready to move forward in the process of being recognized as such. That's it.