Apparently yes, their weapons could be used against them, although I have only ever encountered one example of this in the ancient sources,✭ specifically in Apollodorus' Library 1.6.3, wherein Zeus is engaged in a fierce struggle against the humongous, many-armed monster Typhon.
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. Nonnus' Dionysiaca Book 1 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 by 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.
