I am highly skeptical of this "history".
The idea of "inverse square law" originating in anyone other than Newton is absurd - there were NO dynamical laws of ANY KIND before Newton wrote them, and indeed this is his actual achievement - putting down a distinct, well-defined dynamical theory of matter. The whole idea of force itself was invented by him, and indeed the mathematical method to describe it.
Newton antagonized many of his colleagues, who he must have understood were so far behind him that education was hopeless. Newton did not always behave in the most straightforward manner and let his frustrations get the better of him on occasion. But there is not a shred of doubt that "inverse square law of gravity" is Newton's alone. Halley's speculation about "attraction according to the reciprocal duplicate proportion" cannot be called a force law. Indeed while he was speculating about this problem, the solution was already known to Newton, who had tired of battling with the loudmouth Hooke (the string theorist of his day), had withdrawn and refused to publish his work. Halley deserves great credit for putting up with the nearly paranoic Newton and in getting him to come out of his shell and explain his work. This was the real origin of the Principia, and Halley's actual contribution.