The description exactly matches a decent biography of Newton's that I read recently. Hooke had good intuition and nothing else. He guessed what the right law of gravity was, and knew what he'd have to show to show that it was right. However it was all guesses, Hooke didn't have the mathematical techniques to tackle the problem. He just had good intuition and a big mouth.

Newton had been over the same territory decades earlier, with the right math, and enough elbow grease to back it up. There is no question that Newton had the result long before Hooke's boast. Furthermore Newton seems to have suspected that Hooke couldn't have come up with that guess, and believed that Hooke must have stolen it somehow from Newton.

This took place, of course, after Hooke and Newton had already tangled about optics. That Halley got Newton to admit to having a proof, and further got Newton to publish it is a testament both to Halley's dedication and some luck. It probably helped that Newton tried to prove his point by sending a "challenge" to the Royal Society, one which Newton made a mathematical mistake in his treatment of, and one which Hooke guessed right. (The challenge was that under an inverse square law, when an object is dropped, does it actually fall straight down? Hooke guessed the right answer from Kepler's laws.)

Newton's public embarrassment may have played a role in Newton's decision to produce as comprehensive a work as he did. There is no question that Newton's irritations over Hooke's past quibbling and grandstanding was part of why Newton deliberately made the Principia hard to read. Newton wanted to make sure that anyone who wanted to comment had to READ the blasted thing first. (He says as much in letters to people.)

Cheers,
Ben