The big question with all ancient descriptions is how it is ever possible to know whether they are "accurate" and to what extent they describe "reality". Until an actual example of the Claw dated to the late 3rd century BC is excavated at Syracuse, we can never be absolutely sure; all we have to corroborate the evidence of one written account is the evidence of another written account. You'll have to decide for yourself whether you find such evidence persuasive or not.

That said, the Roman siege of Syracuse is unusually well-attested. We have no fewer than 3 detailed accounts of Marcellus' initial assault on the city:

• Polybios 8.7 (2nd century BC)

• Livy 24.34 (around the year 0)

• Plutarch, Life of Marcellus 15.1-4 (2nd century AD)

Of these, Plutarch is the furthest removed from the events, having been writtenover 300 years after the siege. Unlike Polybios (and, to a lesser extent, Livy), Plutarch was not a historian, but a moral philosopher; his intention in writing the Lives was to provide the Greco-Roman elite with examples of admirable and questionable conduct. I'm surprised the site you mentioned uses his account, among the three surviving ones, as the base of its claims.

This is all the more puzzling since all three accounts clearly go back to the same source. The similarities are too many to be a coincidence. They all mention Archimedes and his role in the defence of the city. They all feature more or less the same details in their accounts of the initial attack by sea. Most tellingly, they all progress in the same way: they start with Roman overconfidence in their approach to the walls, then show Romans being massacred from afar by bolt-shooters and stone-throwers, then move on to Romans being slaughtered from engines hidden in the wall and firing unseen from arrow loops. Finally, they describe Archimedes playing another trump card as the Roman ships came up to the walls themselves: cranes fitted to the top of the walls threw heavy stones and weights of lead down onto the decks, while other cranes brought down the Claw, which seized hold of ships and lifted them out of the water.

Other machines which he invented were directed against storming parties, who, advancing under the protection of penthouses, were secured by them from being hurt by missiles shot through the walls. Against these he either shot stones big enough to drive the marines from the prow; or let down an iron hand swung on a chain, by which the man who guided the crane, having fastened on some part of the prow where he could get a hold, pressed down the lever of the machine inside the wall; and when he had thus lifted the prow and made the vessel rest upright on its stern, he fastened the lever of his machine so that it could not be moved; and then suddenly slackened the hand and chain by means of a rope and pulley. The result was that many of the vessels heeled over and fell on their sides: some completely capsized; while the greater number, by their prows coming down suddenly from a height, dipped low in the sea, shipped a great quantity of water, and became a scene of the utmost confusion.

-- Polybios 8.7.8-11

As for the ships which came closer, in order to be inside the range of his artillery, against these an iron grapnel, fastened to a stout chain, would be thrown on to the bow by means of a swing-beam projecting over the wall. When this sprung backward to the ground owing to the shifting of a heavy leaden weight, it would set the ship on its stern, bow in air. Then, suddenly released, it would dash the ship, falling, as it were, from the wall, into the sea, to the great alarm of the sailors, and with the result that, even if she fell upright, she would take considerable water.

-- Livy 24.34.10-11

After Marcellus' attack was utterly defeated by these engines, he retreated and settled in for a long siege.

Given the similarity of these accounts, it would be prudent to follow the earliest one (Polybios, who is also generally the most reliable of the three for Greek and for military affairs) and to consider the others only insofar as they alter or add further information.

Either way, it seems Plutarch was on firm ground when he summarised what his own sources told him. We may question the reality of some of the less well-attested inventions of Archimedes, such as the mirrors with which he was supposedly able to set ships on fire from a distance; but the Claw is safely embedded in all of our evidence for the Roman siege of Syracuse.