I don't know and I don't care what [Nature editor] Maxine means by "open" or "free". I care what the BBB [Budapest-Bethesda-Berlin] Declarations mean. Peter is not defining terms however he likes; he is working with published, widely accepted definitions. He is well within his rights to expect that other people will indeed use the same definitions: that is, after all, the point of having developed and published them. Nature does NOT have "many open access projects and products", it has one (barely) OA journal and the excellent Precedings, together with a number of commendable free-to-read initiatives (blogs, Nature Network, the various free-to-read web special collections, etc). "Open Access" is not a fuzzy buzzword that Maxine is free to define as she sees fit, and if she is going to start abusing it as marketing for Nature then she most certainly does need telling off.
Which is all rather similar to a discussion taking place in the computer world about who has the right to call themselves "open source".