I don't know anything more about this than the two links you just posted, but the article in the Independent and the Politifact Fact Check certainly do not come to the conclusion that this "declaration" is fake.
The Independent piece is talking about some of the 150,000+ names signed by the public. Of course people on the Internet are going to add fake names to the list. That doesn't make the declaration fake.
The Politifact piece explicitly notes that the official signatories are real. It then goes into an explanation of why their heterodox opinion is wrong, which maybe it is. But that doesn't make it fake.
The Independent piece is talking about some of the 150,000+ names signed by the public. Of course people on the Internet are going to add fake names to the list. That doesn't make the declaration fake.
The Politifact piece explicitly notes that the official signatories are real. It then goes into an explanation of why their heterodox opinion is wrong, which maybe it is. But that doesn't make it fake.