Examples in which this happens in a couple of stories✭ seem to indicate that: Yes, their weapons could be used against them.
> Artemis smacked upside the head with her own hunting-gear
Book 21 of Homer's Iliad narrates a scene from the Trojan War in which the Olympian deities are fighting amongst themselves, with some of them doing so in support of the Trojans as they oppose their fellows who are backing up the Greeks.
Artemis, the goddess of the hunt, faces off against her own stepmother Hera, the queen of the gods. Hera (in between Lines 477 & 501), annoyed that the younger goddess would dare to challenge her, tells Artemis off, and then she grabs both the wrists of the huntress in her own left hand, while, with her other hand, she
snatched Artemis' bow and its gear from her
shoulders and, laughing all the while, boxed her on the ears with these self-same
weapons as she twisted this way and that,
scattering the winged arrows. Artemis fled weeping from her... She
took her tears with her, but left the bow and arrows where they lay.
Artemis's humiliation continues (Lines 502-513) in a practically comical tone as she scurries off to her dad Zeus's house on Mt Olympus to cry in his lap about what has just happened (and Zeus, even though he "clasped her to him," merely shrugs off her report with a chuckle).
Meanwhile Hermes, who had been squared off against Artemis's mother Leto, throws his hands up in the air, declining to fight the Titaness since, in his own words, it looks like a tough job "trading blows with the wives of Zeus". Leto, for her own part, then wordlessly proceeds to gather "up the curved bow and the arrows that had fallen hither and thither amid the whirl of dust, and went off carrying her daughter’s weapons."
> Zeus incapacitated after forced surgery using his own sickle-sword
Set earlier on in Zeus's career, in rather more grave circumstances, Apollodorus' Library 1.6.3 narrates a story that seems to depict the king of the gods almost actually getting killed by the humongous, many-armed monster Typhon.
In the fierce struggle between them, Zeus' two means of battling the monster are his thunderbolts, which he uses as long-range missiles, and an unbreakable sickle, which he uses to lash out at close quarters. When the fight brings the two combatants to Mt Casius in Syria, Typhon is by now severely wounded. Nonetheless he uses the snake-like coils of his many arms to entwine Zeus so that he wrests the sickle from the god's grasp and uses the weapon to tear out the sinews or tendons from the Olympian king's hands and feet, thus paralysing him.
Zeus is eventually rescued from this ignominious capture by his sons Hermes and Aegipan. The sickle is never again mentioned. Incidentally an unbreakable sickle appears one other time in the same book, earlier on, towards its beginning (1.1.4). There, prior to Zeus's birth, his father the Titan Cronus is supplied by Gaia, the Earth, with this device in order for him to castrate her husband Uranus, the Sky.
It is tempting to see a connection between Cronus's sickle and the one used later by his son, but we can only speculate as to whether they are one and the same, since we are not granted such a detail. There is also no occurrence, as far as I can tell, of a story in which Poseidon's Trident is ever handled by anyone other than him; nor of a myth in which Zeus's thunderbolts are disapprovingly in someone else's possession.
The only occurrences I know of someone else handling Zeus's thunder and lightning (apart from the manufacturers thereof) are: when Zeus let his baby son Zagreus play with the thunderbolts and sit on his throne—from which Zeus suffered no harm at all; and when Zeus was pelting Typhon with thunderbolts. Some of the ones from Typhon's battle fell astray into the sea, where they were received by the marine gods Poseidon and Nereus. Book 1 of Nonnus' Dionysiaca tells us simply that the weapons "fell into the welcoming hand of Poseidon", after which we never hear of them again; or that "old Nereus brought the brine-soaked bolts to the ford of the Cronian Sea [apparently the North Sea, by Northern Europe], and dedicated them as an offering to Zeus."
Both Zeus's thunderbolts and Poseidon's Trident seem to me to be merely concretised expressions of the powers of these gods. In ancient art they are depicted wielding these attributes of theirs in much the same way that modern professional wrestlers and comicbook superheroes wear colourful costumes: it is so that they can be easily and correctly identified by the audience which is consuming this media.
In the narrative world of the mythology, my guess would be that these particular weapons were designed such that only their rightful owners possessed the ability to use them. As far as Zeus' thunderbolts are concerned, therefore, I suppose that I agree with the premise proposed in the quote from your Question, even though Ethan and I are merely speculating here.
I do not, however, perceive the same issue with Medusa's head to be quite as simple, for various reasons, such as the fact that Medusa was not originally a weapon owned by Athena, not to mention the fact that the whole tale which has Athena angrily metamorphosing a beautiful maiden Medusa into a monster Gorgon seems to be the invention of late classical poets. In the more ancient accounts Medusa is simply born a Gorgon. At any rate, as referenced in your inquiry, that is a whole other Question.
✭ I have confined my Answer to Greco-Roman sources since your Question seems to be specifically about Greek mythology.
