About the principle I described? I suggest you do some reading.
Yes, because this is an obvious straw man argument that at best just shows you don't understand what you are responding to.
We can obviously have vampire books and movies without it being pulled from Anne Rice, because obviously vampires preexist Anne Rice. But, if we observe fiction which contains elements about vampires that did not exist before Anne Rice wrote her stories, then we can conclude that that fiction descends not from vampire fiction generally but from Anne Rice specifically. So, yes, we can tell whether or not a piece of fiction was influenced by and owes its existence in part to Anne Rice's highly influential works. And likewise, we can tell whether the piece of vampire fiction is influenced by other highly influential works. For example, if we see a close association between bats and vampires, then we can be almost sure that the fiction was influenced by Bram Stoker's Dracula, because Bram Stoker mistranslated the word for 'moth' as 'bat' when researching his story. You might object that the writer was influenced to associate bats and vampires by tales of the vampire bat, but then you'd have to note that the 'vampire bat' was not even called the vampire bat until 1901 - four years after the publication of Dracula - even though it had been known to science for almost 100 years before that.
No, your post is speculation. I have textual evidence. You have offered none. Moreover, you are citing the existence of a tale of the Arabian Nights that so far as I can tell does not exist. The Rocs of the Arabian Nights do not offer benevolent aid in stories that I'm familiar with, but rather carry off sailors inadvertently when the sailors strap themselves to carcasses.
First, #2 is clearly bogus. There are almost no elements common between say the 5th voyage of Sinbad and Tolkien's giant eagles, other than that both are large birds. But more to the point, neither of your speculations are what is at stake.
What you have to show is that the Monster Manual would end up with BOTH an entry for Roc and an entry for Giant Eagle without the influence of Tolkien, and that the entry for Giant Eagle - whatever it's source material - would have been familiar to the writer of the Monster Manual and suggested to them 'Chaotic Good' as an alignment. All I have to show is that the Roc entry clearly conforms to the description of the Roc of Arabian story and so is almost certainly derived from the Arabian stories, and that the Giant Eagle clearly conforms to the description of the Giant Eagles of Tolkien's stories and so is almost certainly derived from the Tolkien stories.
The existence of the two entries speaks for itself, and to my mind settles the question all by itself. No reader of the Arabian Nights alone would be likely to independently imagine two different types of 'Roc', name one of them independently 'Giant Eagle', and also independently imagine them as just large enough to bear a rider but not an elephant and as being generally benevolent. Nor is it reasonable to suppose that this hypothetical inventor in the 1970's is familiar with the Arabian Nights tale but not with Tolkien and is not influenced by Tolkien in his creation of the 'Giant Eagles'.
And further, until you actually show me this hypothetical story of rocs rescuing sailors on purpose because they are benevolent (and not trying to eat a sheep or cow carcass that the sailor has tied themselves to), your theory that Tolkien is influenced by the Roc of Arabic lore and not by more proximal Eurpean ideas like Zeus's companion/sevant the Aetos Dios. Recall if you will that unlike the Roc, the Giant Eagles of Tolkien are the servants of Manwe the 'god' of the sky, and kind of the 'gods' in Tolkien's legerdemain.
