I follow Yes fairly closely, and the original diagnosis for Jon Anderson was that he was done as far as singing / touring / performing goes. Now, maybe he, being an amazingly positive person, wishes to believe otherwise, but the word on the Yes web site at the time was that Yes was pretty much through.
If the other guys decide to carry on without him, although I personally don't see it as being "authentically" Yes, then that's their call, I suppose. I mean, in reality, Yes has been through numerous personnel changes through the years, and Howe, Wakeman and White aren't even original members themselves, so there you go.
After all, Yes did put out an album without Jon Anderson previously. This isn't the first time they've toured without him.
Out of the loop? I didn't know there was a loop!